Transformer questions

[rattus]

Huh?

Roger, whatever you are trying to say, I am saying King's results are wrong regardless of the method used.

King should explain why the load currents are not equal to the phase currents in this case. That would be far more meaningful than a reference to symmetrical components or fancy analysis programs.

BTW, I am a firm believer in such software having done hundreds of SPICE simulations in the past, but I would not use SPICE on such a simple problem.

 

[winnie]

I am having difficulty understanding this thread as well, but I'd like to make a stab at it.

Roger, are you saying that the software that King is using may be producing results which are _acceptable_ for the industry in which they are applied, even though there is an obvious mathematical error? In particular, all of the various job specifications and tolerances (required safety factors), combined with the fact that loads are generally far more balanced than this example suggests, mean that any errors caused by the assumption of a balanced load are much smaller than the allowed tolerance.

Second, are you saying that King may not be allowed to analyze or even discuss errors of math in the software that he is using?

I agree with rattus and others; the symmetrical results presented by the software that King is using are not the correct answer to the original question. However I see this as a useful example of the reality that all the calculations that we do are simply approximations of reality. By using more complex calculations we may better approximate reality, but a poorer approximation may be 'good enough'. It is also a useful cautionary tale: software embodies the approximations selected by the designer of the software; one should always treat the results with some suspicion, especially in limit cases where some basic assumption might fall apart.

-Jon

 

[winnie]

Stiff, we know that the phase difference in the two currents is 120 degrees, therefore we add them vectorially,

I = 2.5A x 1.732 = 4.33A

Rattus,

I went back and looked more closely at the numbers. I believe that for the case of feeding the 208V single phase load, the primary currents should be 2.5A, 2.5A, and 5A.

Since all current is flowing through the same single phase load, the current flow in coil A is in phase with the current flow in coil B. The primary currents should also be _in phase_, so the vector addition of the two 2.5A primary currents gives 5A.

In the case of the two separate 120V 10A loads, then the primary currents have their normal 'balanced' phase relation, and are not in phase, and I get the same 2.5A, 2.5A, 4.33A that you got.

-Jon

 

[kingpb]

How can you possibly say that a 10A load @208V = 2080W, or 2080VA w/ pf=1, and a (2) 10A loads at 120V = 2400W or 2400VA w/ pf=1 are going to have the same current draw of 2.5A at 480V.

2080VA/(480V*sqrt 3) = 2.5A

2400VA/ (480*sqrt 3) = 2.9A

Also, if you arn't using symmetircal components to solve this, then your doing it wrong.

 

[rattus]

Oops!

Oops!

Rattus,

I went back and looked more closely at the numbers. I believe that for the case of feeding the 208V single phase load, the primary currents should be 2.5A, 2.5A, and 5A.

Since all current is flowing through the same single phase load, the current flow in coil A is in phase with the current flow in coil B. The primary currents should also be _in phase_, so the vector addition of the two 2.5A primary currents gives 5A.

In the case of the two separate 120V 10A loads, then the primary currents have their normal 'balanced' phase relation, and are not in phase, and I get the same 2.5A, 2.5A, 4.33A that you got.

-Jon

Yer right!

 

[rattus]

How can you possibly say that a 10A load @208V = 2080W, or 2080VA w/ pf=1, and a (2) 10A loads at 120V = 2400W or 2400VA w/ pf=1 are going to have the same current draw of 2.5A at 480V.

2080VA/(480V*sqrt 3) = 2.5A

2400VA/ (480*sqrt 3) = 2.9A

Also, if you aren't using symmetircal components to solve this, then you're doing it wrong.

How you ask?

First, in either case, only two transformers are active. The third can be ignored.

Second, The PF of the load can be unity, but the PF seen at the primaries in the first case is 87%! Then,

Preal = 480V x 2.5A x cos(30) + 480V x 2.5A x cos(30) = 2078W

Sqrt(3) appears as 2 x cos(30) here.

Third, the PF at the primaries is unity for the second case. Then,

Preal = 480V x 2.5A x cos(0) + 480V x 2.5A x cos(0) = 2400W

Sqrt(3) is not a factor here!

King, 99% of engineers don't use or even understand symmetrical components, so why insist on applying this method to the simplest of problems? We can get the right answers with a lead pencil and a used envelope if we remember the value of cos(30).

 

[kingpb]

First, how is the power factor on the hv side of the transformer suddenly 87% when the load is 100%. I hope your not trying to say that because of the 30 degree shift on a delta/wye transformer, the shift modifys the power factor? The 30 degree shift causes the voltage and currents on the HV side to be shifted 30 degrees from the LV side, but it does not change the angle relationship between the voltage and current, and therefore the pf would be ideally the same (barring impedance of transformer). If that's the case, then a wye/wye transformer would have a different answer.

Second, regardless of whether or not people understand symmetrical components, the issue is they are specifically derived for dealing with unbalanced polyphase systems (in the electrical world, 3-phase). Of which, a 208V single phase load on a three phase system falls into that category. It is incorect to treat unbalanced loads by using balanced system formulas.

I agree, you can get to the correct answer with a pencil and any used envelope, simply (alright, not so simple) by knowing the PROPER symmetrical component power formulas and using matrix algebra. I simply prefer to use a calculator and computer, in place of a slide rule.

Didn't anybody realize the reason you can't readily find info about unbalanced loads is becasue they are not something everybody is capable of simply busting out a text book calc on.

That's why people come up with "fudge factors" to use. It's sorta like faith and UFO's, you just gotta beleive!

 

[steve66]

Winnie got it right.

Since you only believe in UFO's and computer generated models Kingpb, here is proof just for you: Analyisis with SKM software showing the correct results. This agrees with Winnie's back of the envelope calculation that you say can't be done:

http://i49.photobucket.com/albums/f252/Sragan/results.jpg

http://i49.photobucket.com/albums/f252/Sragan/schedule1.jpg

http://i49.photobucket.com/albums/f252/Sragan/Schedule2a.jpg

http://i49.photobucket.com/albums/f252/Sragan/Schedule2b.jpg

 

[kingpb]

I cannot disput the results of the software, becasue I do not have the program and cannot verify how it treats an unbalanced system or what input data was used.

Also, I am still trying to find the hand calcs that you say winnie did, please point me in the right direction because I am not seeing them.

I did not say hand calcs couldn't be done, get your facts straight.

Finally, Steve, it's interesting that you posted winnie's answers, and yet you have not contributed to this topic other then to try and dispute everything.

Maybe you should not be so quick to take credit for someone else's (i.e. winnie's) work, unless of course you two are one in the same.

Apparently there are enough experts in this forum, good luck to all.

 

[steve66]

I cannot disput the results of the software, becasue I do not have the program and cannot verify how it treats an unbalanced system or what input data was used.

Strange, because you keep posting your software results as if they were gospel.

Also, I am still trying to find the hand calcs that you say winnie did, please point me in the right direction because I am not seeing them..

Winnie didn't post his entire calculation, but he posted enough for Rattus to follow. His last post details the calculations.

I did not say hand calcs couldn't be done, get your facts straight.

No, you said "if you aren't using symentrical components, you aren't doing it right". Then in your next post, you said hand calculations required "symetrical components and matrix algebra."

Finally, Steve, it's interesting that you posted winnie's answers, and yet you have not contributed to this topic other then to try and dispute everything.

I have only posted to this thread twice. Once to tell you your answer was obviously wrong. And once to support Winnie's correct answer. And I did contribute by showing software calculation that support the correct answer.

I think you just cannot accept the fact that you were wrong. But we now have three other people that agree on the correct answer. Therefore, I probably won't see the need to post to this thread again.

 

[engy]

Apparently there are enough experts in this forum, good luck to all.

I hope this does not mean you are leaving for good.
No one is trying to prove anyone wrong, just trying to get the right answer.
I've been burnt a few times myself.

There is a lot of good discussion here, a great place to learn.
I wish I had more time to contribute.

Mike

 

[hardworkingstiff]

I hope this does not mean you are leaving for good.
No one is trying to prove anyone wrong, just trying to get the right answer.
I've been burnt a few times myself.

There is a lot of good discussion here, a great place to learn.
I wish I had more time to contribute.

Mike

Ditto!

Don't leave king.

 

[rattus]

First, how is the power factor on the hv side of the transformer suddenly 87% when the load is 100%. I hope your not trying to say that because of the 30 degree shift on a delta/wye transformer, the shift modifys the power factor? The 30 degree shift causes the voltage and currents on the HV side to be shifted 30 degrees from the LV side, but it does not change the angle relationship between the voltage and current, and therefore the pf would be ideally the same (barring impedance of transformer). If that's the case, then a wye/wye transformer would have a different answer.

King, you answered your own question. With a resistive line to line load, we see 30 deg phase shifts between the secondary phase voltages and currents. This shift does indeed modify the power factor! That is the fallacy in your argument. Yes, the PF of the load itself is unity, but the PF of the xfrmr and load is 87%.

Then each transformer delivers,

Preal = Vphase x Iphase x cos(30) = 120V x 10A x cos(30) = 1039W

At the primary,

Preal = 480V x 2.5A x cos(30) = 1039W.

As Winnie points out, the line currents are 2.5, 5.0, and 2.5A.

The phase difference appears when we take the difference between two voltage phasors separated by 120 deg. The primary connections have no effect.

This question could easily be taken from an AC Circuits exam. Too bad, I think no one teaches AC Circuits nowadays.

Software is wonderful, but one should always be sure that the results make sense. Otherwise, your results may be wrong, and you'll never know why!

 

[winnie]

kingb,

You cannot find the calculations that I did because I did not post them. I posted a description of the physical system that pointed to the results that I got, and I posted the results, but I did not 'show my work'.

Rattus presumably checked my results by doing his own calculation, and steve66 posted both the inputs and results from a particular piece of software, which agree with the answer that I gave.

This does not mean that I believe that symmetrical components is an incorrect way to solve this problem, far from it. The method of symmetrical components is probably the most efficient way to solve these problems when designing real systems. However this is _not_ the only method to use, and for this exceedingly simplified and explicitly unbalanced example, other methods provide the answers more simply and with less chance of error. Basic vector math may be used. The approach of examining each and every circuit, figuring the vector current for each circuit, and then adding these up would not scale well to a full system design, but it is a correct approach.

Somewhere in your calculations, the necessary information that the system is not balanced is being lost. I presume that this is an error in the software that you are using, because the method of symmetrical components should be able to deal with this.

To answer your question above:

How can you possibly say that a 10A load @208V = 2080W, or 2080VA w/ pf=1, and a (2) 10A loads at 120V = 2400W or 2400VA w/ pf=1 are going to have the same current draw of 2.5A at 480V.

There is a trick in the question: the power factor of 1. The _load_ has a power factor of 1, meaning that the current through the load is in phase with the voltage difference between terminal A and terminal B of the transformer. But the current through the coils of the transformer is _not_ in phase with the voltage developed across the coils of the transformer.

We have three voltages to consider Vab, Van and Vbn. These are 208V, 120V, 120V respectively. These are each at their own phase angle. I_load is in phase with Vab, and thus not in phase with Van nor with Vbn.

In both the 10A 208V example, and the dual 10A 120V example, you have 10A going through the two secondary coils, and thus 2.5A though each primary coils. This is true in both cases. However the phase angle of the current flow, and thus the power factor, is different between the two cases, and in neither case is the power factor actually unity on all of the supply conductors.

-Jon

 

[rattus]

Winnie, I agree with you almost. I contend that in case two, phase voltages and currents are in phase--unity PF that is.

 

[winnie]

How about this:

For case two:
the current through the secondary coils is in phase with the voltage induced in the secondary.
the current through the primary coils is in phase with the voltage applied to the primary coils.
the three phase feeder to the primary is not carrying balanced current, and thus current may be out of phase in whatever is supplying the 480V.
if the 480V source is a wye source, then the two 2.5A phases will have non-unity power factor.

Better

-Jon