# Transformer Calculations

#### jreay

##### Member
Hello,

I'm new to posting here, but have came here a few times when i have been stuck on questions..

I'm currently doing my 3rd year technical training, transformer and motor heavy.

The parts that i'm getting stuck on are the transformer calculations. We don't get examples on them.

The question that i'm stuck on is:

"It is desired to transform 100KW at unity power factor from 23,000V to 2300V by means of an open-delta open-delta transformer bank. Calculate the transformer primary phase current."

I'm not quite sure where to start..

Thanks,

Jeff

#### Smart \$

##### Esteemed Member
From our perspective, this is a "homework" question... so rather than providing you with the answer, we will help you draw on your knowledge to arrive at the answer yourself.

First, do you understand what is meant by "an open-delta open-delta transformer bank"?

#### jreay

##### Member
From our perspective, this is a "homework" question... so rather than providing you with the answer, we will help you draw on your knowledge to arrive at the answer yourself.

First, do you understand what is meant by "an open-delta open-delta transformer bank"?
From my understanding it is a bank of transformers with a primary side in open delta(one phase missing/open) and secondary side also open-delta.

#### jreay

##### Member
Because i'm a new member do my posts take time to appear?

#### Dennis Alwon

##### Moderator
Staff member
Because i'm a new member do my posts take time to appear?

Yes but they should appear immediately now

#### Smart \$

##### Esteemed Member
jreay said:
Smart \$ said:
Transcribed from PM
jreay said:
From my understanding it is a bank of transformers with a primary side in open delta(one phase missing/open) and secondary side also open-delta. One phase has been disconnected so say A-B would be Open or B-C or C-A.
Correct.

Three conductor primary, three conductor secondary, essentially two single phase transformers supplying three phase power.

Now if primary is 23,000V and secondary is 2300V, what is the turns ratio of primary to secondary winding?
We would have a ratio of 10:1.
Correct.

FWIW, I see the question posed as a loaded question, but to tell you in what manner would provide the answer without you actually learning anything. So...

The question makes you think about how three phase power is provided by two single phase transformers connected as an open delta/open delta bank.

When discussing power supplied by an open delta bank, what is the first thing that comes to mind (beyond what I just wrote above)?

#### Smart \$

##### Esteemed Member
Posted by PM before my last post here....

jreay said:
100,000 / (2300 x 1.732 x pf 1) = 25.102 / 10

= 2.510A per phase.

Correct?

#### jreay

##### Member
Correct.

FWIW, I see the question posed as a loaded question, but to tell you in what manner would provide the answer without you actually learning anything. So...

The question makes you think about how three phase power is provided by two single phase transformers connected as an open delta/open delta bank.

When discussing power supplied by an open delta bank, what is the first thing that comes to mind (beyond what I just wrote above)?

That the transformers are operating at 57.7% of the original apparent power capacity?

#### Smart \$

##### Esteemed Member
jreay said:
100,000 / (2300 x 1.732 x pf 1) = 25.102 / 10

= 2.510A per phase.

Correct?
Correct.

ETA: Note you should not write two equations into one line...

100,000 / (2300 x 1.732 x pf 1) = 25.102
25.102 / 10 = 2.510A per phase.

That the transformers are operating at 57.7% of the original apparent power capacity?
That is the answer I was searching for (though I'm not absolutely sure it is worded correctly). But you already answered the question posed.

For bonus points , what would be the minimum kVA rating of the two single phase transformers to supply the 100kW load?

Last edited:

#### jreay

##### Member
Correct.

That is the answer I was searching for (though I'm not absolutely sure it is worded correctly). But you already answered the question posed.

For bonus points , what would be the minimum kVA rating of the two single phase transformers to supply the 100kW load?
How would you word it properly? lol

That's another question i have, if i have 2.51A/phase then VA per phase is 5773VA. Since there's only 2/3 phases then i multiply 5773 by 2?

11.546KVA?

#### Smart \$

##### Esteemed Member
...That's another question i have, if i have 2.51A/phase then VA per phase is 5773VA. Since there's only 2/3 phases then i multiply 5773 by 2?

11.546KVA?

If kVA is equal to kW at unity power factor, how are you going to get 100kW of power from 11.546kVA?

#### Smart \$

##### Esteemed Member
I'm not sure im grasping this... If i have 100,000KW at unity, i also have 100,000VA. Even if i take that 100,000 x .866 or 100,000 x .577. I am getting the wrong answer.

Edit: nevermind.. I type .566 into my calculator.
You have 100kVA supplied/delivered through three line conductors, but you only have two winding pairs...

#### jreay

##### Member

If kVA is equal to kW at unity power factor, how are you going to get 100kW of power from 11.546kVA?
You're not .

Is there a general approach to take when you're given a transformer question? In regards to any configuration??

Wye-Wye, Delta-Wye, Wye-Delta, etc..

#### Smart \$

##### Esteemed Member
You're not .

Is there a general approach to take when you're given a transformer question? In regards to any configuration??

Wye-Wye, Delta-Wye, Wye-Delta, etc..
It seems we are getting a bit off track, and to answer this question will take us us the long way to answering my question.

You were on the right track with your 11.546VA answer but used the wrong voltage multiplier and factor in your equation. Also, for clarification, I am asking what the minimum kVA rating is for one transformer. Not both combined.

There are a few ways to calculate this, and I implied your 2.51A primary line current is correct. You stated it as 2.51A/phase... but you don't have all three windings. It helps to distinguish between line current and phase current, and in this case, 2.51A is line current but not phase current... but with only two windings, all the line current from the open ends has to go through both windings. So if you have 2.51A of line current through a 23,000V winding, what is the kVA?

#### jreay

##### Member
It seems we are getting a bit off track, and to answer this question will take us us the long way to answering my question.

You were on the right track with your 11.546VA answer but used the wrong voltage multiplier and factor in your equation. Also, for clarification, I am asking what the minimum kVA rating is for one transformer. Not both combined.

There are a few ways to calculate this, and I implied your 2.51A primary line current is correct. You stated it as 2.51A/phase... but you don't have all three windings. It helps to distinguish between line current and phase current, and in this case, 2.51A is line current but not phase current... but with only two windings, all the line current from the open ends has to go through both windings. So if you have 2.51A of line current through a 23,000V winding, what is the kVA?
Can approach it two ways.

Either 100,000 x .577(57.7%) = 57700KVA
or 23,000V x 2.51A = 57730KVA

#### Smart \$

##### Esteemed Member
Also, FWIW, here's a graphic which depicts line, phase, and winding currents... Last edited:

#### jreay

##### Member
Correct BTW, latter answer should be the same as former using 3 significant figures.

FWIW, 57.7% is 1/?3...

100,000 ? ?3 = 57,735.0kVA
Thank you for all your help.

Do you know of any places online to get a better understanding of transformer calculations in a general?