Dear James,

At this juncture, i think i would have to infer that the textbook phasor diagrams do not depict increase/decrease in magnitudes of Ea, Eb and Vt to retain simplicity or clarity in explanation.
Please correct me if i am wrong. Any additional inputs/suggestions in this regard are welcome.

P.S. My heartfelt condolences to the victims of the terrible forest fire in Australia. May their souls rest in peace!

Thanks mate. It is pretty intense indeed. I'm actually Canadian though, so luckily, excuse the selfishness, I have no close friends or family here. I guess it should have been expected after the hottest heatwave since 1855 followed by a day of 47-48 degrees celcius.

Not sure what to tell you. Perhaps the textbook talks about speed regulation. I can't really say much else until you scan/post the article.

 

Thanks mate. It is pretty intense indeed. I'm actually Canadian though, so luckily, excuse the selfishness, I have no close friends or family here. quote]

Dear James,
In your public profile you have mentioned Melbourne! so, i thought you were Australian.

 

aye, I live here. It is intense even if I'm not australian.

 

OK two generators running in synchronicity.

The voltage ouputs, Ea and Eb are the same. The phasor diagram is as shown. Ea and Eb are real quantities.

Now introduce a small perturbation. Hughes carefully sidesteps the fact that the phasors move to have both real and imaginary components as the maths is too difficult for the level in his book. However they are no longer equal, and if you look carefully he does not say they are equal.

So long as they remain nearly equal equality and synchronicity can be is restored by exchange of energy.

If extra torque is applied to generator A this will advance the phase of Ea.
Similarly reducing the torque to B will retard the phase of Eb. Both relative to the bus.

This will drive a current Ic = (Ea-Eb)/(Za+Zb) around the local circuit identified by Hughes. If Ea was not different from Eb then Ic would be identically zero. Note also that these are now complex voltages, currents and impedances. Ic is lagging nearly 90° behind (Ea-Eb), but nearly in phase with Eb.

I should add that the bus voltage does not change. Ea (Eb) is slightly larger (smaller) but its projection on the bus remains the same when you do the vector sum. Perhaps this is what was confusing you?

Thus A experiences a retarding torque, which is generating and B receives an accelerating torque which is motoring, restoring the equality.

 

I should add that the bus voltage does not change. Ea (Eb) is slightly larger (smaller) but its projection on the bus remains the same when you do the vector sum. Perhaps this is what was confusing you?

Dear Studiot,

Thanks. But this statement directly contradicts the analogy provided by Davebee of a 'two pedalled bicycle' in the earlier posts in this thread, wherein applying this analogy to the '2 PM alternators in parallel query', all the voltages would increase!

Please note:-The 2 PM alternators are not connected to the power grid (infinite bus), but is considered to be supplying its own independent resistive load (hence the bus voltage cannot be considered as constant).

So, now i am unable to infer whether i should follow the practical explanation given by Davebee (analogy with 2 pedalled bicycle), or follow the theoretical explanation depicted by the textbook phasor diagrams.
Please help me out!

Kind Regards,
Shahvir

 

There is no imaginary part to pedalling a bicycle.
It is hard work.

 

If you were to answer some of my questions, we might be able to proceed further.

For instance did you understand Hughes description about a (Kirchoff) loop, independant of the bus bars?

Did you understand my comment about the bicycle?

 

If you were to answer some of my questions, we might be able to proceed further.

For instance did you understand Hughes description about a (Kirchoff) loop, independant of the bus bars?

Did you understand my comment about the bicycle?

Dear Studiot,

I have not referred to Hughes for the simple reason that the phasors provided by him is exactly the same as found in most textbooks (also which i happen to refer to). It's not about authors, its the phasor theory as presented in textbooks in general.

Sorry, I am not aware of the Kirchoff loop.

To be honest, i did not understand about your comment about the bicycle!

1) It might be that the increase/decrease in voltages would be transient in nature and hence would not have been possible to be represented in the form of phasor diagrams. Is my assumption valid ? Please comment.

2) Also, Davebee's analogy would be valid (for increase/decrease of voltages) if the perturbation would persist for a long duration or would have been intentional in order to change the 'load sharing' between the two alternators! Please comment.
Sorry for trouble, very grateful.

Thanks & Regards,
Shahvir

 

I should add that the bus voltage does not change. Ea (Eb) is slightly larger (smaller) but its projection on the bus remains the same when you do the vector sum. Perhaps this is what was confusing you?

Dear Studiot,

I think you are right! perhaps its the way in which the vectors are projected which might be the source of my confusion.

Also, the magnitudes of the voltages seem to be unchanged (constant) just by observing the phasor diagram.

Kind Regards,
Shahvir

 

i.e. if we trace the closed circuit formed by the two generators...........it is more convenient to consider these emfs in relation to each other than to the bus bars...

Does this not describe a loop around which we can apply Kirchoff's Voltage Law?

 

The bicycle is a purely mechanical system. As such there are no complex quantities involved in its mechanics, no real and imaginary components.

In an electrical system the quantities - current, voltage , impedance, reactance etc have real and imaginary components. They are all functions of a complex variable.

So ask yourself what happens to the generator voltage when you apply extra torque to the generator.

The real component, in phase with the bus, remains constant.
The imaginary component, at 90° to the bus, increases slightly from zero to some small value.
Thus the resultant is now slightly larger and slightly out of phase.

This resultant is applied to the Kirchoff loop, in opposition to the second generator voltage.

The result is controlled by the equation Ic = (Ea-Eb)/(Za+Zb) I quoted earlier. Note these quantities are all complex.

 

Thus the resultant is now slightly larger and slightly out of phase.

This resultant is applied to the Kirchoff loop, in opposition to the second generator voltage.

The result is controlled by the equation Ic = (Ea-Eb)/(Za+Zb) I quoted earlier. Note these quantities are all complex.

Dear Studiot,

I have no issues with the theoretical part. But the resultant becoming large (increase in magnitudes of the resultant voltages) is not depicted in the phasor diagrams! This is the problem.

Kind Regards,
Shahvir

 

becoming large

Oh come on, I used the words 'increases slightly'.

Your ruler must be better than better than mine when applied to a small diagram in a page margin. I certainly couldn't say just how long the vector arms are - and I have the original. My own sketches were diagramatic not to scale.

 

Here is a situation to be answered. The torque applied to Alternator A is large enough to significantly increase its speed.

Does the following hold:

- A will begin to generate for B.
- B will begin to motor.

Will they both now operate faster than the initial condition? Lets assume their velocities are not controlled externally.

Does an increase in speed of a generator not increase the voltage?

 

Here is a situation to be answered. The torque applied to Alternator A is large enough to significantly increase its speed.

Does the following hold:

- A will begin to generate for B.
- B will begin to motor.

Will they both now operate faster than the initial condition? Lets assume their velocities are not controlled externally.

Does an increase in speed of a generator not increase the voltage?

Dear James,

Please do not misunderstand me. I agree with the theory that as alternator speed increases, magnitudes of voltages Ea, Eb and Vt will also increase!

My only problem is that this increase (variations) in the magnitudes of the said voltages is not directly depicted in the associated textbook based phasor diagrams.
Hence, i requested Studiot to confirm whether the phasor diagrams only depict transient (or perturbation) conditions ?

Thanks & Regards,
Shahvir

 

Shavir,

I'm getting rather fed up with doing all the work here especially as I still don't know where you are coming from on this.

The detail you seem to be seeking and some of your questions are at a level taught at university mid-term degree or end-term college diploma level in Electrical Engineering. Either way it fills large textbooks. This depth is not normally taught in Physics courses. I don't know if you are a Physicist with an interest, a student Electrical Engineer or just curious.

I can guess that you are on the Indian sub continent and have less resources than we in the West. Also your first language is probably not English. So the quality of your English and your politeness does you great credit.

But I still don't know whether you know or understand what a complex number is, or can do circuit analysis using them. Indeed some of your questions imply a much lower level of knowledge.

You have posed a question about coupled oscillators. These appear in many guises in different branches of the physical world, in fireflies, chemical reactions, mechanical systems, and of course electrical generators.

Nature is a wonderful creature and she allows such oscillators to exchange energy to pull separate oscillators into synchronisation. The mechanism is different for each type, of course.

There are limits to this phenomenon as well and I have repeatedly stated that deviations must be small. There is no intrinsic requirement for the deviation to be short lived or transitory however. In the case of the two generators generator A can continue to make up a shortfall from generator B indefinitely, so long as A is supplied with extra power. In fact a process of oscillation, called hunting, is perfectly possible where A and B exchange roles and energy. This is undesirable and real world machines are fitted with extra windings to prevent this.

With regard to the generators, an increase in torque implies an increase in shaft speed and thus frequency. A small increase in frequency is the same as a phase advance.

If we allow the generator speeds to drift too far apart, beat frequency components begin to appear as in attachment 1.

If we allow the speeds further apart still we reach a situation as in my example in attachment 2. There is now no coupling between the oscillators, they can be considered as separate machines.

Now is the time for you to do some work.

Can you draw the phasor diagrams for machine A and B?

Do you understand the complex equation

V = E ± RI ±jXI

and can you apply it to the circuit in attachment 2?

 

Dear Studiot,

Your frustration is justified and for that, I apologize! I would say your guess is correct. I do not wish to hide anything from you. I am an Electrical Engineer working as a maintenance engg. in a reputed company in the Indian sub continent.

You are right when you say I have had limited access to resources compared to you guys in the West and in the bargain, end up questioning my level of knowledge. Whatever my limitations, I will attempt to answer your questions to the best of my abilities, but please give me some time.

My intention was to only question the practical implications of textbook phasor diagrams thru these discussions and not stir up some kind of controversy. My query was simple; Why are variations in alternator voltages not represented in textbook phasor diagrams inspite of the associated theory depicting otherwise.

I may not match the level of knowledge you guys possess, but my interest in Electrical Science is what drives me to know more or gain a refreshing insight into the EE topics of my interest and for that I am prepared to face any number of insults or brickbats I receive! ( If it ain't broke, fix it until it is)

P.S. If you guys think I am some kind of an irritation or an annoyance who is hell bent on disturbing your peace, please let me know! However, that is not my intention. I would even back out from this forum if you guys do not wish to converse with me!

Thanks & still Kind Regards,
Shahvir

 

So now we know some detail, stop apologising and let's get down to work. Wanting to know more is an admirable trait. Good on you.

Whilst it is, in principle, possible to accurately draw phasor diagrams to scale and use these to perform calculations, I can't imagine anyone doing this these days.

However phasor diagrams (call them sketches really) are useful to clarufy what is going on. Any that I might draw have the simple purpose of helping getting the signs right in a calculation. So I would regard textbook ones as 'diagramatic', rather than perfect copy. especially when they are usually pretty small scale and will be distorted by printing in average cheap texts. At one time engineering textbooks often had useful graphs and diagrams you could accurately scale from. These graphs were much used before the widespead use of calculators and computers, but such textbooks carried a premium price because of the special printing needed to ensure accuracy.

So to work

Did you understand what I said about the difference between small, medium and large variations?

Let us know how you get on with the complex / phasor in the second attachment. We are happy to help, but there is no point offering this unless it helps.

 

Did you understand what I said about the difference between small, medium and large variations?

Let us know how you get on with the complex / phasor in the second attachment. We are happy to help, but there is no point offering this unless it helps.

Dear Studiot,

What i understand of small variations is that there is a temporary disturbance but the alternators still remain synchronized.
Medium variations would be when the torque disturbances are large causing large oscillations (hunting) but both alternators still remain synchronized.
Large variations would mean torque disturbances are so large as to break the synchronous bond between the two alternators causing severe mechanical stresses!

I wish you would throw some light on the concept of 'unequal load sharing' between two PM alternators i.e. if one alternator is taking more load than the other intentionally, by increasing the input torque to any one PM alternator.

For the reply to your 2nd attachment, please give me some time.

Thanks & Regards,
Shahvir

 

Dear Studiot,

Attached is a set of phasor diagrams as per my interpretation of the ckt. diagram in attachment no. 2 sent by you.

Fig (a) represents the phasor diagram if we consider the magnitude and phase of the voltages and currents as seen by the external (load) ckt. As the input torque to Alt ‘A’ is increased, induced EMFs Ea > Eb which is represented by an increase in the magnitude of vector Ea (Eb being the reference vector). Also, Ea leads Eb as input torque to Alt ‘A’ > Alt ‘B’.

Both alternators would settle at a higher speed (busbar frequency). This would also result in an increase in the terminal voltage Vt across load, since Ea and Eb also increases (due to overall increment in the speed of both the alternators).

Ec is the resultant voltage due to Ea and Eb where; Ec = Ea – Eb

‘I’ is the circulating current which appears in the local loop due to resultant voltage Ec (since no-load operation is considered). 'I' is considered to be in-phase with Ec due to stator impedances Ra and Rb being purely resistive.

Fig (b) depicts the same conditions as above, but the electrical quantities presented are as seen by the local (internal) loop.

P.S. The textbook phasor diagrams show magnitude of vector EA = magnitude of vector Eb.

Kind regards,
Shahvir