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

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LongCircuit

Member
Location
Trinidad & Tobago
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?

Transformer_79A24E7C-5056-8D7B-05FB33580E049B49.jpg

Thank you in advance.
 
Smart $

Smart $

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

Ingenieur

Senior Member
Location
Earth
Need to think about it
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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Smart $

Smart $

Esteemed Member
Location
Ohio
Phil Corso said:
LongCircuit,

Please assign current values to IR, IB, IW!

Phil Corso
Click to expand...
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.
 
T

topgone

Senior Member
LongCircuit said:
Say RW is 75kVA, and the other two are 50kVA each...
Click to expand...

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

kwired

Electron manager
Location
NE Nebraska
LongCircuit said:
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

Thank you in advance.
Click to expand...
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.
 
L

LongCircuit

Member
Location
Trinidad & Tobago
kwired said:
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.
Click to expand...


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.
 
I

Ingenieur

Senior Member
Location
Earth
Phil Corso said:
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
Click to expand...

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
no centertap/n loads

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

Phil Corso

Senior Member
Location
Boca Raton, Fl, USA
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
 
L

LongCircuit

Member
Location
Trinidad & Tobago
Phil Corso said:
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
Click to expand...

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