Mate, just apply some of the analogies provided into excel and plot the unit circles of each. Derive the overall phasors from them.

An example I gave earlier should provide this easy enough if you simplify the system through assumptions provided.

I don't really get why you are after phasors so much. It isn't even a very practical system. The phasors would only be important if you were trying to maintain a given output voltage at varying torques through some form of variable control on both Alternator A and B.

Since this does not seem to be the case, just simplify the system, plot Alternator A and B outputs in excel and derive the load phasor.

Any realistic scenario which may sound interesting would be actively controlled and try to cancel out any torque, and subsequently frequency, differences such that the load voltage could be held constant, just provide more power.

 

Dear Skeebopstop,

Thanks for your reply. I do not wish to be stuck on phasors, thanks to the subsequent discussions on this thread, i have come to understand the impracticality of the phasor system.

I was referring more so to Davebee on the phenomenon of 'Armature Reaction' wherein, according to textbook theories, there seems to be a decrease in the terminal voltage 'Vt' when the input torque (and hence loading) of Alt 'A' is increased! I had hoped that he would be able to comment on the same.

Kind Regards,
Shahvir

 

Shavir,

I don't know what books you have been reading but I suggest you get hold of a copy of

Electrical Technology by Edward Hughes.

This is the classic textbook on the subject and I am appending an extract from the 6th edition. The book was originally published as 'Electrotechnology' and contains a wealth of information that you seem to bee seeking, some of it very practical. later editions have introduced semiconductors and digital circuits, so will not be so relevant to yourself.

 

Dear Studiot,

Thanks for considering my request. As far as my query on the value of Alternator induced EMFs Ea, Eb and terminal voltage Vt is concerned, it is solved due to Davebee’s excellent analogy of the two pedalled bicycle! However, I would want to point out that the query itself arose due to the confusion as regards the phasor diagrams identical to the ones you have sent me.

Let me clarify, again;
As per Davebee’s analogy, induced EMFs Ea , Eb and terminal voltage Vt would all increase, along with suitable variations in the load angle σ (and busbar frequency). However, if you observe the attached phasor diagrams, the magnitudes of induced EMFs Ea and Eb remain constant, albeit with variations in the load angles! The magnitude of terminal voltage Vt would have been considered as constant, if available in the diagram. This should not have been the case, practically, as I am considering the two PM alternators on finite busbars i.e. not connected to the local power grid (infinite bus). Please comment on the same.

P.S. Thanks very much for your suggestions on the reference materials, extremely grateful.

Kind regards,
Shahvir

 

Dear Skeebopstop,

Thanks for your reply. I do not wish to be stuck on phasors, thanks to the subsequent discussions on this thread, i have come to understand the impracticality of the phasor system.

I was referring more so to Davebee on the phenomenon of 'Armature Reaction' wherein, according to textbook theories, there seems to be a decrease in the terminal voltage 'Vt' when the input torque (and hence loading) of Alt 'A' is increased! I had hoped that he would be able to comment on the same.

Kind Regards,
Shahvir

Assume Vt is a maximum when Ea and Eb are in phase and assume the magnitude of Ea = |Eb| , i.e. Vt = |2*Ea|.

Consider Alternator A has a bit more torque applied, so that it begins to go slightly out of phase with B. Assume for now that Ea and Eb are still equal in magnitude, just slightly out of phase (i.e. Ea is spinning slightly faster now than Eb). Therefore, the 'best case |2*Ea| no longer exists, as some of the power is becoming reactive due to phase lead/lag. So your 'real' load voltage seen has nowhere to go but down.

My assumption that the magnitude of Ea will remain the same with increased speed is invalid. I do however believe, that in no practical generating situation, would the speed increase be enough to generate enough 'real' voltage to compensate for the reactive powr loss due to being out of phase, even if Fa = 2*Fb (Frequency), a situation which would harmonically align much better than anything where Fb < Fa < 2*Fb.

I think you'll have to verify my last statement though, and assume that Fa = 2*Fb and work out if Vt actually does work out on average to be less. RMS values won't apply rather you'll have to integrate Vt to confirm.

 

Consider Alternator A has a bit more torque applied, so that it begins to go slightly out of phase with B. Assume for now that Ea and Eb are still equal in magnitude, just slightly out of phase (i.e. Ea is spinning slightly faster now than Eb). Therefore, the 'best case |2*Ea| no longer exists, as some of the power is becoming reactive due to phase lead/lag. So your 'real' load voltage seen has nowhere to go but down.

Actually, this is what is depicted in the textbook phasor diagrams, wherein Ea, Eb and Vt are considered to be constant (the only variation being load angle σ) and the cause of my doubts!

Also, how did you arrive at the expression Va - Vb = Vload ? Please comment.

Thanks & Regards,
Shahvir

 

Please ignore Va-Vb = Vload, that is an oversimplification of this sytem.

Here is an article that might help:

http://canteach.candu.org/library/20030804.pdf

Considering the great extents practical generators go through to keep their generators 'synchronized' (i.e. the same speed), I would disagree with your text book. See phasors in presentation.

 

Dear James,

Thanks very much for the link. I think it was suggested earlier by Davebee in connection with alternator connected to large power grid (Infinite bus). Hence, all voltages of the said alternator would be held constant as speed (and hence frequency) cannot change due to the 'synchronous locking' of the alternator with the large power grid (Infinite bus).

P.S. Refer Page 2 of this thread, post # 17. Also, refer my reply to the same i.e. post # 18 and please comment on the same. Also, please refer the textbook attachment forwarded by Studiot, post # 24. This attachment is what i am referring to in my query.

Kind regards,
Shahvir

 

Write the author of the textbook. As far as I can see, also seemingly so in the literature I posted, what your book says is not the case. Perhaps you are wording it to us differently however than the book intends, at which point you'll have to scan the article or contact the author.

 

Write the author of the textbook. As far as I can see, also seemingly so in the literature I posted, what your book says is not the case. Perhaps you are wording it to us differently however than the book intends, at which point you'll have to scan the article or contact the author.

Dear James,

I was referring to the attachment sent by Studiot, post # 24 of this thread. The phasor diagram clearly indicates magnitudes of Ea and Eb is considered to be constant, with variations in load angle only. Please comment in this regard.
Sorry for trouble!

Thanks & Regards,
Shahvir

 

Do you understand the first part about the E.M.Fs generating equally to the busbars, but being negative to each other? That is an important point and you must understand this first.

 

Do you understand the first part about the E.M.Fs generating equally to the busbars, but being negative to each other? That is an important point and you must understand this first.

Dear James,

The 1st part is very well understood by me, because these diagrams are extensively used in almost all the textbooks to explain 'parallel operation of two alternators'.

The 2nd part is where there is variation of input torque of one of the alternators, but still the magnitude of Ea and Eb remains constant. This is the source of my doubt! I humbly request you to comment for the 2nd part.

Thanks & Regards,
Shahvir

 

The second part is an instantaneous race condition which isn't actually true but useful in describing what happens. Studiot's article gets cut short prior to mentioning this.

Regardless, the scenario in my opinion is this. Eb loses torque due to steam loss. This causes the rotor to slip a bit. If this rotor slip were to continue it would result in a frequency/speed drop and subsequently the phasor magnitude. 'However', what in reality happens as you see in Studiot's post, is that Ea actually starts to drive Alternator B as a motor, in particular since they are synchronized at this instance.

This then 'pulls' Alternator B back in phase with Alternator A. Now, lets say that this extra load on Alternator A to drive Alternator B like a motor caused Alternator A to 'slip'. Yes, the frequency of both will stay synchronized but reduce. If the frequency were to drop, although Ea = Eb, their magnitudes would be less than their original starting points. This I believe is what got cut off at the end of the page from Studiot's post, that Alternator A, in order to maintain the initial magnitude of Ea, must be driven with more torque to compensate and maintain the frequency, as per the article I posted.

 

Studiot's article gets cut short prior to mentioning this.

Yes because I was encouraging you to try and obtain/borrow a copy of a standard text.
It would not be fair to lift whole sections.

 

Aye, I only mentioned it as I can't 'concretely' say, but the article you posted seemed to be confirming what I had been speculating from the beginning.

I'll leave it up to Shahvir to do the digging if he doesn't trust my intuition

 

Sorry I meant I was trying to encourage Shavir to look at Hughes text.
I chose that one in particular as it answers many of the other questions he is asking at the level he seems to be working at.

 

Sorry I meant I was trying to encourage Shavir to look at Hughes text.
I chose that one in particular as it answers many of the other questions he is asking at the level he seems to be working at.

I hate reading textbooks God I was one annoying student!

 

The second part is an instantaneous race condition which isn't actually true but useful in describing what happens. Studiot's article gets cut short prior to mentioning this.

Regardless, the scenario in my opinion is this. Eb loses torque due to steam loss. This causes the rotor to slip a bit. If this rotor slip were to continue it would result in a frequency/speed drop and subsequently the phasor magnitude. 'However', what in reality happens as you see in Studiot's post, is that Ea actually starts to drive Alternator B as a motor, in particular since they are synchronized at this instance.

This then 'pulls' Alternator B back in phase with Alternator A. Now, lets say that this extra load on Alternator A to drive Alternator B like a motor caused Alternator A to 'slip'. Yes, the frequency of both will stay synchronized but reduce. If the frequency were to drop, although Ea = Eb, their magnitudes would be less than their original starting points. This I believe is what got cut off at the end of the page from Studiot's post, that Alternator A, in order to maintain the initial magnitude of Ea, must be driven with more torque to compensate and maintain the frequency, as per the article I posted.

Dear James/Studiot,

I apologize you guys had an argument due to me!
James, so you mean to say it is a transient condition which causes temporary disturbances in the speed (frequency) and magnitudes of Ea and Eb, and then all the parameters would regain their original conditions?

Also, if i were to consider the same phasor diagrams for the condition of 'increase in input torque to any one alternator', what would be your inference on this as regards the behaviour of the phasors pertaining to the magnitudes of Ea and Eb in the second part? Please comment and elaborate on the same, if possible.
Sorry for trouble!

P.S. It is not my intention to stretch this thread too far, purposely! Its just a humble attempt by me to try and relate the theoretical concepts to the practical conditions with the help of knowledgeable experts like you guys.

Hence, i chose to take the discussion on the relevance of the textbook related phasor diagrams a bit further! Lets hope something fruitful comes out of these discussions.

Thanks & Regards,
Shahvir

 

I believe, if you were to increase the steam flow of one alternator without increasing the loading, it would speed up. It still would synchronize with the other mode and the two would run a bit faster and their voltages subsequently increase.

I cannot confirm this until you scan in your complete article or find the remainder of Studiot's textbook posting.

 

I believe, if you were to increase the steam flow of one alternator without increasing the loading, it would speed up. It still would synchronize with the other mode and the two would run a bit faster and their voltages subsequently increase.

I cannot confirm this until you scan in your complete article or find the remainder of Studiot's textbook posting.

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!