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

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Ingenieur

Senior Member
Location
Earth
This is convincing. I'd like to see how I can arrive at that identity matrix though. I know it's a bit extra writing, but do you mind posting the steps. it will help be grasp it better.

I did it thru inspection
ia = -1 iac + 0 icb + 1 iba
so first row = [-1 0 1]
and so on

the inverse is indeterminate
So no go

took another approach (matrix but simpler)
think I got it
using my conventions from above
and Ia = 300, Ib = 275 and Ic = 250 at 0, 120, 240 deg respectively
I get iac = 161 ang -51

a few others had a solution
I'll post mine after they share lol
 

Phil Corso

Senior Member
GentlePeople...

Wrong, wrong, wrong!

One doesn't need to know more than arithmetic! Hogwash to identity matrix, and xfmr %Z! And, more importantly ignore the Load!

Will reveal answer tomorrow... must first check with my lawyer to insure I'm not releasing proprietary info!

Phil
 
I did it thru inspection
ia = -1 iac + 0 icb + 1 iba
so first row = [-1 0 1]
and so on

the inverse is indeterminate
So no go

took another approach (matrix but simpler)
think I got it
using my conventions from above
and Ia = 300, Ib = 275 and Ic = 250 at 0, 120, 240 deg respectively
I get iac = 161 ang -51

a few others had a solution
I'll post mine after they share lol


Well this is the most progress so far.
 

Ingenieur

Senior Member
Location
Earth
GentlePeople...

Wrong, wrong, wrong!

One doesn't need to know more than arithmetic! Hogwash to identity matrix, and xfmr %Z! And, more importantly ignore the Load!

Will reveal answer tomorrow... must first check with my lawyer to insure I'm not releasing proprietary info!

Phil

Easy to say 'wrong' when you post no answer
just give 1 phase current, show no work
no one will know your proprietary method

I did not use xfmr Z or load, both are accounted for in the line currents
assumed no neutral
V does not matter (until kva is calculated)
phasing 0/120/240
 

kwired

Electron manager
Location
NE Nebraska
GentlePeople...

Wrong, wrong, wrong!

One doesn't need to know more than arithmetic! Hogwash to identity matrix, and xfmr %Z! And, more importantly ignore the Load!

Will reveal answer tomorrow... must first check with my lawyer to insure I'm not releasing proprietary info!

Phil

Thanks

Don't get arrested!
I took it to mean he has a patent, top secret information, or even something that may effect national security on how to calculate this and only he/his company has rights to use those methods.:huh:

Unfortunately I don't have an advanced math degree of any sort and this is all somewhat over my head on how to determine this, but Phil apparently is the only person that has legal rights to the solution anyway:)
 

Ingenieur

Senior Member
Location
Earth
Using my convention and magnitude/ang
and
ia = 256/0
ib = 294/120
ic = 341/240

iac = 178/-74
icb = 213/176
iba = 160/47

I need to check my math tomorrow
 

topgone

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 15212

Thank you in advance.
Please do the math here: Page 108 to 110 of this reference LINK

I did my own calcs using the %Z = 1.81% for each of the 2-50kVA transformer and 1.784%Z for the 75 kVA transformer and my phase currents are:
Phase A and B (50's) = 57.5966% of line current
Phase C (75kVA) = 58.01% of the line current.
Above calculations are based on a condition where the line currents are equal.
 

Ingenieur

Senior Member
Location
Earth
checked my math, made a small math error
all 3 phases offset by -67 deg to normalize ph at 0
assumed V = 240

iab = 160/0...... 38.5 kva
ibc = 185/120...... 44.4 kva
ica = 178/-140...... 42.7 kva

curious what others come up with
the sequence varies from my previous because I oriented ph seq differently

the avg of the above Ph currents x sqrt3 = 301 A
the avg of the measured line currents = 297 A
 
Last edited:
checked my math, made a small math error
all 3 phases offset by -67 deg to normalize ph at 0
assumed V = 240

iab = 160/0...... 38.5 kva
ibc = 185/120...... 44.4 kva
ica = 178/-140...... 42.7 kva

curious what others come up with
the sequence varies from my previous because I oriented ph seq differently

the avg of the above Ph currents x sqrt3 = 301 A
the avg of the measured line currents = 297 A

Yes. V = 240 Forgot to mention that.
 

Phil Corso

Senior Member
Ladies and Gentlemen,

Although InJunEar's calculation of the load's phase-currents is an incorrect approach, he's on to something!

Now, calculate total kVA using the average of Line-currents, Ib, Ir, Iw!

Phil
 

gadfly56

Senior Member
Location
New Jersey
Occupation
Professional Engineer, Fire & Life Safety
Ladies and Gentlemen,

Although InJunEar's calculation of the load's phase-currents is an incorrect approach, he's on to something!

Now, calculate total kVA using the average of Line-currents, Ib, Ir, Iw!

Phil

So far you've been all hat and no cattle. You said you were going to share some super duper analytical method. Time to pony up before others here head back to the chalk board.
 

Ingenieur

Senior Member
Location
Earth
So far you've been all hat and no cattle. You said you were going to share some super duper analytical method. Time to pony up before others here head back to the chalk board.

when I check my work by adding my phase currents up to calc line currents they are within an acceptable margin of error

he is not helpful, not sure why
he makes claims
says people are wrong
but never offers a solution
must not have talked to his lawyer ;)


avg line current 297
kva = 123.4 kva
not sure what that does for us

if you take the avg line current of 297 and do this:
ph current = 1/1.732 x act line current/avg line current x act line current you get
Iac = 0.577 x 256/297 x 256 = 127 A....30.5 kva
Ibc = 168 A....40.3 kva
Ica = 226 A....52.2 kva
total kva 123
same as the avg line current yields

but this not take into account phasing
 

Smart $

Esteemed Member
Location
Ohio
checked my math, made a small math error
all 3 phases offset by -67 deg to normalize ph at 0
assumed V = 240

iab = 160/0...... 38.5 kva
ibc = 185/120...... 44.4 kva
ica = 178/-140...... 42.7 kva

curious what others come up with
the sequence varies from my previous because I oriented ph seq differently

the avg of the above Ph currents x sqrt3 = 301 A
the avg of the measured line currents = 297 A
Your phase vectors aren't adding up to the line vectors. For example, should work out that Iab - Ica = Ia

160V@0° – 178V@-140° = 318V@21° (approx.)
 
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