# How to calculate if one transformer of a three phase Star/Delta bank is overloaded?

#### topgone

##### Senior Member
Isn't S known?

It is P and Q which are not, correct?

Does it really matter regarding winding phase current?
You nailed it. Windings are rated in kVA or just amps!

#### Phil Corso

##### Senior Member
InJunEar...

See, others are learning! Here's the rest!

Part 1, only V and A are known, so S (Apparent Power) = V x A = 126 x 56.3 = 7,150 VA!

Part 2, since P = 1,182 W (Real Power) is now known, then Q (Reactive Power) = Sqrt(S^2 - P^2) = 7,052 VAr!

I hate to ask the following of you, but since you didn't participate, how about revealing the load's power-factor... lagging or leading (decimal or %'s acceptable)!

Phil

#### Smart \$

##### Esteemed Member
InJunEar...

See, others are learning! Here's the rest!

Part 1, only V and A are known, so S (Apparent Power) = V x A = 126 x 56.3 = 7,150 VA!

Part 2, since P = 1,182 W (Real Power) is now known, then Q (Reactive Power) = Sqrt(S^2 - P^2) = 7,052 VAr!

I hate to ask the following of you, but since you didn't participate, how about revealing the load's power-factor... lagging or leading (decimal or %'s acceptable)!

Phil
Whoa! Whoa!

We know S, and not P or Q, is what I said. How did we jump to knowing P in Part 2?

Ingenieur cannot tell you the load power factor because it has not been stated or otherwise established. For his calculations, he in effect stated the phi as an assumed 0°/120°/240° respectively. However, in this case, phi and load power factor (or rather arccos thereof) are not necessarily, likely not the same thing.

#### GoldDigger

##### Moderator
Staff member
Isn't S known?

It is P and Q which are not, correct?

Does it really matter regarding winding phase current?
As written, only the magnitude of S is known.

If the phase offset on one L-L current is different than that of another connected to the same line it affects the magnitude of the corresponding L-N current and vice versa.

#### Smart \$

##### Esteemed Member
As written, only the magnitude of S is known.

If the phase offset on one L-L current is different than that of another connected to the same line it affects the magnitude of the corresponding L-N current and vice versa.
I am aware of that. Please keep the response simple. S* [scalar value; magnitude, if you will] is known, correct? P* and Q* are not, correct?

*If we knew P or Q we could establish S vector.

How is knowing P and /or Q relevant?

What would knowing P and/or Q change?

#### GoldDigger

##### Moderator
Staff member
I am aware of that. Please keep the response simple. S* [scalar value; magnitude, if you will] is known, correct? P* and Q* are not, correct?

*If we knew P or Q we could establish S vector.

How is knowing P and /or Q relevant?

What would knowing P and/or Q change?
It is not relevant as long as the phase angle of all three loads is the same.

#### Smart \$

##### Esteemed Member
It is not relevant as long as the phase angle of all three loads is the same.
I assume you mean the same phi (difference of current to voltage angle).

You do realize the probability of that being the case for unbalanced current magnitudes is quite, quite low, right there next to improbable, right?

#### Phil Corso

##### Senior Member
Fellas...

I'm not going to play your game of Obfuscation (typical of most engineers)! If anyone is interested in what I call "Vectors from Magnitudes" contact me off-forum!

Regards, Phil Corso

#### Sahib

##### Senior Member
Good day, all.I require assistance in determining how to calculate whether one transformer in a three phase star/delta bank is overloaded based on the line current on the delta side (load side).I know that I can simply have a lineman take readings at the transformer at the X1 or X3 terminals, but I need to know how to calculate it.So for example, let's say that the bank consists of 50,75, 50 kVA transformers, and the line currents on the delta (load) side are taken to be 256A, 294A, 341A, how do I work out the phase currents in the delta side of the transformer?View attachment 15212Thank you in advance.
You want only phase current magnitudes. Kirchoff current law is applicable to both dc and ac circuits. So it should be applicable in an ac circuit with effective dc values only. So by considering line currents as dc values and replacing transformers by ideal dc sources (as a first approximation ) and by applying Kirchoff current law, equivalent dc phase current and so solution to your problem may be found.

#### Sahib

##### Senior Member
You want only phase current magnitudes. Kirchoff current law is applicable to both dc and ac circuits. So it should be applicable in an ac circuit with effective dc values only. So by considering line currents as dc values and replacing transformers by ideal dc sources (as a first approximation ) and by applying Kirchoff current law, equivalent dc phase current and so solution to your problem may be found.
Sorry. I committed blunder: Kirchoff law cannot be appled that way..................Well another try. Suppose phase sequence of line currents is known. Then line currents can be represented in trigonometric form as functions of time. Each line current may also be represented as difference between respective phase currents also in trigonometric forms by applying kirchoff law. The resulting equations may be solved for an arbitrary instant of time to find intantaneous values of phase currents. From that it is easy to find RMS values.

#### Ingenieur

##### Senior Member
InJunEar...

Your wrong again! Both Q and S can be easily calculated! Knowledge of Xfmr %Z is unnecessary. The effect of %Z is already implicit in the OP's stated line-current values!

Phil
If easy what are they?
|V| 240
Iabc 256/294/341
no phase information known

#### Ingenieur

##### Senior Member
Isn't S known?

It is P and Q which are not, correct?

Does it really matter regarding winding phase current?
You are correct
but with the given info P or Q can't be calculated
either one will give power factor

his example is easily calculated

1812 = 117 x 56.3 x pf
pf = 0.2751
ang = 74 deg
pf delta ang v - i
since v = 127 i = 53
Z = v/i = 2.08/74 Ohm
and
P 1812 given
Q 6332 j
S 6603/74

but the op NEVER gave P , Q or V phase, only V and I which yields a per ph kva
assume load is a ungnded wye
S/ph = 240/1.732 x Ix
frmm the kva a per phase |Z| can be calculated
|Z| = ph kva/V^2

op kva
35.5
40.7
47.25

Z
1.85
2.12
2.46

Iph
148
170
197

no phase info can be determined

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#### Smart \$

##### Esteemed Member
Whoa! Whoa!

We know S, and not P or Q, is what I said. How did we jump to knowing P in Part 2?
...
AHA! I traced his "example" back to post #75.

Simple answers are best. It seems no one knows how to do that.

You are correct
but with the given info P or Q can't be calculated
either one will give power factor

his example is easily calculated...
So it's just another "if" scenario that leads us nowhere, right?

I've often said people have a tendency to tell on themselves:
Fellas...

I'm not going to play your game of Obfuscation (typical of most engineers)! If anyone is interested in what I call "Vectors from Magnitudes" contact me off-forum!

Regards, Phil Corso

#### Ingenieur

##### Senior Member
AHA! I traced his "example" back to post #75.

Simple answers are best. It seems no one knows how to do that.

So it's just another "if" scenario that leads us nowhere, right?

I've often said people have a tendency to tell on themselves:
I'll buy anyone a beer (craft import to boot!) who can get mr phil to answer my question
:roll:

If a tree falls in the forest what is the power factor?

#### Smart \$

##### Esteemed Member
I'll buy anyone a beer (craft import to boot!) who can get mr phil to answer my question
:roll:

If a tree falls in the forest what is the power factor?
You have to be in the forest when the tree falls to hear his answer. :happyyes:

#### Ingenieur

##### Senior Member
You have to be in the forest when the tree falls to hear his answer. :happyyes:
if that is the case I may jump into the trees fall path
I could not bear another imaginary watt meter postulation

#### Phil Corso

##### Senior Member
InJunEar,

Just contact me off-forum!

Phil

#### Sahib

##### Senior Member
Hi folks! If each line current is known in trigonometric or vector form i.e if its intantaneous value as a function of time is known or if at least sufficient number of intantaneous values of each line current are known,then the phase currents may be found out.

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#### iwire

##### Moderator
Staff member
InJunEar,

Just contact me off-forum!

Phil
Phil this is lame.

You keep telling posters they are wrong but you won't go into the reasons why or show how you feel it can be done.

#### Sahib

##### Senior Member
Peace! The solution to OP is in post 138.