Internal Voltage generated

[Zach Stone P.E.]

Lol I am not confused, you are!!!. Anyways.

Just here to help

Given base values 250 KV, 100 MVA and Xd= 1.1 pu,  steady state current =.97 pu

To find per phase Internal Generated Voltage?

pu internal generated Volatge= I*Xd=1.1*.97=1.067pu

Correct. I am in agreement with you here.

Internal generated Line to Line Volatge (6.7% more than base) = 1.067*250=266.75 kV

Internal generated voltage tends to be a per phase quantity, I think the issue is assuming that it is line to line.

Internal generated Phase Voltage=266.75/sqrt3= 154kV

This is not necessary since we've already calculated the internal generated phase voltage in the previous step.

To arrive at the correct answer according to the author of this problem, than you need to use the given base value along with the internal generated phase voltage per unit quantity that we calculated in the previous step.

Make sense?

A great resource for these problems is Wildi's Electrical Machines Drives and Power Systems if you are looking for additional examples.

 

[TNPE]

No one has given credence to my points raised previously.  Right or wrong, a confirmation of the winding configuration is necessary to determine what the "phase" voltage generated actually is?  I didn't get a chance to review today, but as previously stated, the winding configuration will dictate how this problem should be treated.  I don't feel the need to drudge up the basic 3-phase analysis scenarios for wye/delta, and the associated differences with phase and line quantities in voltage and current with each respective configuration.  That said, does the problem statement indicate the configuration?  If not, you can't answer this problem with certainty!!  Unless someone can convince me otherwise, I'll stay put where I'm at.

 

[rg1]

No one has given credence to my points raised previously.  Right or wrong, a confirmation of the winding configuration is necessary to determine what the "phase" voltage generated actually is?  I didn't get a chance to review today, but as previously stated, the winding configuration will dictate how this problem should be treated.  I don't feel the need to drudge up the basic 3-phase analysis scenarios for wye/delta, and the associated differences with phase and line quantities in voltage and current with each respective configuration.  That said, does the problem statement indicate the configuration? No it does not.  If not, you can't answer this problem with certainty!!  Still we can Unless someone can convince me otherwise, I'll stay put where I'm at. It may take time but I will do that.

TNPE, Line configuration in this question is derived from the fact that it is steady state faulty condition of 3 phase bolted fault at the terminals of the generator. The terminal voltage is therefore taken as zero and whole of generated voltage is used to circulate the fault current. The reactance given, Xd, is for one line, as generally given in 3 phase questions(in this case actually it is one phase of the armature of the generator).  The convention  for line configuration is always to take the ckt as star (Y) if nothing is mentioned, for purposes of ease of understanding only, else  you can take it will not effect the results. This I learned when I was in college and I think it is mentioned somewhere in Wildi too.  I will try to give you exact reference.

You do this question by assuming delta connection, the answer to internal phase voltage generated will be same, because in that case the phase current will be reduced by a factor of sqrt3. ( The given reactance is for one phase).

 

[rg1]

Just here to help

Correct. I am in agreement with you here.

Internal generated voltage tends to be a per phase quantity, I think the issue is assuming that it is line to line.

This is not necessary since we've already calculated the internal generated phase voltage in the previous step.

When you posted the below in red color in the your previous post you were right. Now you are wrong. 

For any type of three phase or machine, the ratings and base values can almost always be assumed to be the three phase values unless explicitly stated otherwise. 

For example, if you are sizing a three phase transformer, then you are most concerned with the total three phase power it can deliver - because it is going in a three phase system, and the three phase line to line voltage rating - because it is going to be connected across all three phases.

In this case, it is a three phase generator: 

So the 250kV is assumed to be the line to line voltage, and the 100MVA is assumed to be the total three phase apparent power it will deliver to the three phase system

To arrive at the correct answer according to the author of this problem, than you need to use the given base value along with the internal generated phase voltage per unit quantity that we calculated in the previous step. I will not agree to it till, it fits into the logic. Science is never on a shaky foundation that we change the things at our convenience just to get a figure in the answer. I am not worried about answer to this question, I am worried about what should we take as base Phase Voltage. 

Make sense? One can not do a wrong to arrive at an answer, just because it is in the options, (of course in main exam, something of this kind can be done) we have to get a correct answer and correct answer in this case is 154kV. Authors are not sacrosanct, they are like you and me, anyone including greatest of authors can make a mistake and here in this question he has done it. I found many mistakes in Wildi book too.

A great resource for these problems is Wildi's Electrical Machines Drives and Power Systems if you are looking for additional examples. I generally  go by logic and knowledge I acquired till now but to satisfy you, please see solved problem no. 16-8 at page no. 360 of Wildi book, He has taken per phase value of Voltage to solve similar problem. @TNPE para 8-14 Industrial loads, at page no. 171 in Wildi book says that if nothing is given for consideration of a 3 phase ckt. it can be safely assumed to be a star connected. Not only here, I have seen it at other places also. I will wish to continue the discussion till we decide this question. Now specific references of good ( which have lesser mistakes) text books should be made to prove our point so that the discussion remains fruitful. 

 

[TNPE]

Then if you use that assumption across the board, the generated voltage per phase in this circumstance should be divided by sqrt3.  I don't agree that this assumption is "safe."  It's not like we're working with a motor/generator/XFMR that looks entirely to be an inductive load at start-up, whereby, it is a safe assumption to neglect R and any associated I^2R losses at this given condition.  Furthermore, you have to consider what happens to impedance when you "create" an equivalent wye circuit from a delta, or vice versa.  This problem lacks explicit data IMHO.  This exam is clear and concise.  You will know what they're asking for without having to guess (not to say you can dodge having to use your noggin', cause you can't, but you will be given the appropriate info to solve the problem...along with red herrings and info that's completely unnecessary, just for the sake of tripping candidates up and testing their intuition and subject knowledge).

 

[rg1]

In an earlier post I mentioned

I found many mistakes in Wildi book too.

I correct myself - It is not in the book text, but in some of the Answers to unsolved Questions. 

 

[TNPE]

Well, if I were you and I wasn't given the proper info, I'd be questioning it; but as previously stated, you will be given all necessary info/ratings on this exam.  You will have to make assumptions, but you will know -if you're prepared, well-versed and understand what's being asked for- what assumption should be made by some trigger in the problem statement.  Guessing what winding configuration you're working with is one I can guarantee you will not see.  Now, it's entirely possible a question can be asked in which the winding configuration is completely irrelevant and unnecessary, but that doesn't hold for this given scenario.  At least it doesn't for me, and I have yet to be convinced otherwise.

Put this another way, what is the secondary phase current of a 3-phase, 15MVA, 69kV - 13.2kV XFMR?  Wouldn't you need to know the winding configuration to accurately tell me?  Same applies to this problem, and gross assumptions are simply that, gross!  You want to talk gross and sick, let these assumptions be the difference between you passing or failing the PE..... 

My advice to you and anyone else, don't put too much stock in the veracity and accuracy of practice problems.  If you find a discrepancy, determine why it is a discrepancy and convince yourself of the "right" way to do a problem.  I see erroneous stuff all over this board, and more frequently than should be normal for mass produced texts/materials!!!

 

[cos90]

CI Test 4 Problem 9 is an unfaulted condition, but its base value is taken to mean line to line voltage and is divided by sqrt 3. This is the problem I mentioned earlier.

 

[rg1]

Let me solve the question at hand by assuming connection of the armature winding of the Generator as delta as well as Y connected.

What is the internal generated phase voltage in a 3 phase Synchronous generator. Given base values 250 KV, 100 MVA and Xd= 1.1 pu,  steady state current =.97 pu

 Description- 1. The Xd is always reactance of one of the phase windings of the Generator whether it is delta or star connected. This also appears in the single phase equivalent circuit of the Generator as one phase reactance and I do not think there should be any doubt in this.

                      2. The currents and Voltages are given as Line quantities if not specified otherwise.

A.  Assuming the Generator as Delta connected. 

The phase current will be 0.97/sqrt3= .56 pu giving Eo phase = .56*1.1=0.616pu; resulting generated phase or Line Voltage (Being Delta) =250* 0.616=154kV.

B. Assuming the Generator to be Star connected.

The phase current will be line current and so Eo=1.1*.97=1.067pu; resulting Generated phase voltage to be 1.067*250/sqrt3=154kV.

Does it not make sense. Is there anything wrong with the description 1 and 2.

The example of transformer given by TNPE seems to me out of place mention here?

 

[TNPE]

Is phase voltage in a delta configuration not the same as taking a volt meter and placing the leads across any 2 phases?  If not, then any 3-phase academia I've ever learned has been a farce!!  I've still failed to check this due to being consumed with other things, but Vt (terminal voltage) in a wye is divided by root3 to determine phase voltage (if given line quantities).  You can't "parallel" the familiar power equations to say (i.e. P=sqrt3*V*I*cos(theta) and call it the same thing...not that you explicitly did that, but that's what dots you're practically trying to connect), "see, it's the same."  Still not convinced.....

 

[TNPE]

Nvm, maybe we're making the same argument.  Mea culpa.

 

[TNPE]

I think we're making the same argument, just that I was mistaken due to not fully reading the problem statement.  Since they've provided a base, I would use your approach.  Sorry for the confusion.

Good debate.  Keep the problems coming.  

Since passing the exam, I seem to have a knack for "wanting more."  Blame it on the student in me, but I enjoy tackling problems on this board, and you do a good job of posing some thought provoking scenarios.

 

[rg1]

I think we're making the same argument, just that I was mistaken due to not fully reading the problem statement.  Since they've provided a base, I would use your approach.  Sorry for the confusion.

Good debate.  Keep the problems coming.  

Since passing the exam, I seem to have a knack for "wanting more."  Blame it on the student in me, but I enjoy tackling problems on this board, and you do a good job of posing some thought provoking scenarios.

Thanks, I appreciate it. I too suffer with same syndrome since I do not know when. I enjoy discussions and learn  and refine a lot of concepts during discussions. Problem solving has been my passion and that is why I poke my nose everywhere. I simply, can't stop it. Locked horn is my normal status. I read only concept from the text book and then make formulae satisfying that concept. I generally work the problem from basics and derive formula every time, I do it. I was able to gauge the gap in your concept, there is very very very small gap in full understanding and your understanding; I could feel it, but  there is always a limitation while communicating by messages . I was not able to phrase my replies which satisfies the student in you, of course that was my fault and limitation. Anyways I loved it, I thank you for the positive engagement. Expect a few more sessions like this one.