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

#### LongCircuit

##### 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?

#### Smart \$

##### Esteemed Member
Don't know of any calculation method. We once had a discussion of here about this very thing... with no resolution as I recall.

#### Phil Corso

##### Senior Member
LongCircuit,

As long as there is no current in neutral, and phase voltages are balanced, then there could be a solution!

Regards, Phil Corso

#### Ingenieur

##### Senior Member
should be able to based on simultaneous euqations
differences between line currents ans assumed phase currents (line/1.732)
hmmmm...

Say line a 300
b 250
c 350
phase a-b based on line a 173
based on b 144
Set up 2 sets of equations, one based on line deltas, the other ph deltas

thru iteration adjust one up and the other down for each phase simultaneously til all satisfy
ph a x 0.866 + ph b x 0.866 = line a
same for lines b and c

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#### Phil Corso

##### Senior Member
InJunEar...

Don't you first have to establish a relationship between load-currents, a,b, c, and ph-xfmrs, A-B, B-C, C-A?

Phil

#### Phil Corso

##### Senior Member
LongCircuit,

Please assign current values to IR, IB, IW!

Phil Corso

#### Smart \$

##### Esteemed Member
LongCircuit,

Please assign current values to IR, IB, IW!

Phil Corso
Let me say on his behalf "256A, 294A, 341A" as IR, IB, IW respectively.

Given the variance in line currents, I have to suspect each line has a differing power factor.

#### LongCircuit

##### Member
InJunEar...

Don't you first have to establish a relationship between load-currents, a,b, c, and ph-xfmrs, A-B, B-C, C-A?

Phil
I'm not sure what the relationship is for an unbalanaced load like this. IF the line currents were all the same, the phase currents would be obvious

#### Phil Corso

##### Senior Member
SmartA

Speak again on his behalf: How about ID'ing the Xfmrs!

Phil

#### Phil Corso

##### Senior Member
SmartA

Speak again on his behalf: Can you ID the 3 single-ph Xfmr kVA's?

Phil

#### LongCircuit

##### Member
SmartA

Speak again on his behalf: How about ID'ing the Xfmrs!

Phil
Say RW is 75kVA, and the other two are 50kVA each...

LongCircuit,

Thank you!

Phil

#### LongCircuit

##### Member
LongCircuit,

Thank you!

Phil

You're welcome. I appreciate your help.

#### topgone

##### Senior Member
Say RW is 75kVA, and the other two are 50kVA each...
AFAIK, a 50kVA, 120/208V transformer will have a 1.81%Z while a 75kVA transformer of the same votage rating will have a 1.784%Z. The 75kVA unit, offering a lower impedance take a bigger load share than the two by 50kVA.

#### kwired

##### Electron manager
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 15212

I am going to guess that this is a POCO installation, is 120/240 volts with a high leg system. It probably either feeds one customer with a significant enough 120/240 single phase load that it was decided to use the 75 kVA unit for the side with the neutral but lesser sized units as the three phase load was less, or it serves multiple customers but still has more load on the 120/240 single phase portion of the bank then it has three phase load. You are probably wondering how to determine if the 75 kVA unit is sufficiently sized?

If I am correct so far I would think you want to know some details of the connected loads, not just the connected VA, but demand data from certain loads as well.

#### LongCircuit

##### Member
I am going to guess that this is a POCO installation, is 120/240 volts with a high leg system. It probably either feeds one customer with a significant enough 120/240 single phase load that it was decided to use the 75 kVA unit for the side with the neutral but lesser sized units as the three phase load was less, or it serves multiple customers but still has more load on the 120/240 single phase portion of the bank then it has three phase load. You are probably wondering how to determine if the 75 kVA unit is sufficiently sized?

If I am correct so far I would think you want to know some details of the connected loads, not just the connected VA, but demand data from certain loads as well.

That's correct. But more specifically, I would like to know how to calculate the phase currents in the delta, if for some reason only the line currents to the load were measured, and unbalanced. Most people know how to calcualte this, if the line current/load is balanced. But for some reason schools and universities never focus on unbalanced loads.

That's essentially the crux of the problem.

#### Ingenieur

##### Senior Member
InJunEar...

Don't you first have to establish a relationship between load-currents, a,b, c, and ph-xfmrs, A-B, B-C, C-A?

Phil
Yes
we would need to establish the references
label transformers with kva
relationship to lines
etc

and as you said V's must be balanced

might not be solvable
xfmr Z per kva varies
no way to determine i delta due to xfmr Z or load Z
transformer Z constant? We know not likely
since load Z >> xmfr Z use a standard Z for a given xmfr Z

#### Phil Corso

##### Senior Member
LongCircuit,

It's not taught in school because it involves rather tedious calculation. Especially if the system is unbalanced and only ampere and voltages are known! Thus, vector relationships aren't easily determined... requiring other specific factors!

More later!

Phil

#### LongCircuit

##### Member
LongCircuit,

It's not taught in school because it involves rather tedious calculation. Especially if the system is unbalanced and only ampere and voltages are known! Thus, vector relationships aren't easily determined... requiring other specific factors!

More later!

Phil
I'm intrigued to find out what headway you're making!

???