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

[Ingenieur]

Honestly, i think you've lost me!

You said the problem is "unsolvable" without "load or line phase info" but you question me talking on the same issue? Load info will be manifested on the load current magnitude and the load angle. The scenarios I presented were all about how the load current and their respective angles point into a resolution of the mismatches.

Anyway, I think this is a dead horse already. We might as well stop beating it.

You assigned the phase angles for the line currents as being balanced
they are not, you assumed the imbalance is only based on magnitude not phase
ie only R no X, which likely not the case

niether are the phase voltages balanced which you summed to zero

you set up the system with a predetermined outcome based on the data constraints YOU assigned
not the actual ones for the system (which are unknown)

 

[Smart $]

...
they are not, you assumed the imbalance is only based on magnitude not phase
ie only R no X, which likely not the case

FWIW, two unequal R-only loads can cause a line current phase shift. Take for example an AB-connected 5A purely resistive load and a BC-connected 10A purely resistive load. With respect to "B" line voltage and current, phi is not equal to 0° simply because the loads are not balanced.

The question is, will the transformer phase [i.e. winding] currents be any different if the phase shift is resistive only, reactive only, or a combination of the two?

 

[topgone]

You assigned the phase angles for the line currents as being balanced
they are not, you assumed the imbalance is only based on magnitude not phase
ie only R no X, which likely not the case

niether are the phase voltages balanced which you summed to zero

you set up the system with a predetermined outcome based on the data constraints YOU assigned
not the actual ones for the system (which are unknown)

You meant to say it is not about the load anymore?

 

[Phil Corso]

TopGone,

Now that some of the smoke has cleared, please list the your Delta-Connected load-impedances, Zab, Zbc, and Zca!

Thankyou, Phil

 

[Ingenieur]

You meant to say it is not about the load anymore?

All about the load
you assumed iit to be purely resistive by assigning 0/120/240 to the line i
by doing so you constrained the results
the same of the V sum = 0, unbalanced only due to R or magnitude, no phase

also xfmr Z is 0.01 ohm much less than the load magnitude of 0.75 to 1 ohm
6 unknowns 3 ph i x mag and 3 ph i ang
4 knowns, line i mag x 3 and V mag (assumed for 3 phases)
no phase information
unsolvable

 

[Ingenieur]

TopGone,

Now that some of the smoke has cleared, please list the your Delta-Connected load-impedances, Zab, Zbc, and Zca!

Thankyou, Phil

that is not load Z
that is xfmt pu Z

 

[Phil Corso]

Gentlepeople'

So then, there is still smoke! I just asked for the Load-impedances (presumably delta-connected) or they could just as well be Wye-connected (3-wire of course)

Phil!

 

[Ingenieur]

Gentlepeople'

So then, there is still smoke! I just asked for the Load-impedances (presumably delta-connected) or they could just as well be Wye-connected (3-wire of course)

Phil!

they are unknown
their phase is assumed to be 0/120/240

he used a ratio of xfmr pu Z's to postulate that more current would flow to the lower Z xfmr regardless of the load Z

from an earlier post of his
50 kVA: %IR = 1.1%; %IX = 1.7% or a %Z = 2.02%
75 kVA: %IR = 0.9%; %IX = 1.6% or a %Z = 1.84%

for the 50 kva base Z = 50000/240^2 = 0.868 so Z ohms = 0.0202 x 0.868 = 0.018 Ohm
he may have used the complex form 0.011 + 0.017j, but doesn't matter
it's not the xfmr load that determines line/load current, it's the load! (unless a bolted SC fault lol)
and load Z magnitude 240/254 = 0.945 to 240/341 = 0.704 >>> greater than xfmr Z which could be ignored (and usually is), load/xfmr Z ratio of 40 to 50

 

[Phil Corso]

InJunEar...

Of course the load is unknown! But, I guarantee there is a an unbalanced 3ph, 3w, delta- or wye-load connected to the bus fed by the 3-ph bank! How can you say, the load is ignored!
You have ignored another simple, but very important fact! Power to the load can be calculated using just the info provided by the OP: 1) Source Voltage is 240V because it's a Hi-Leg connection; and 2) Line-Currents in the 3 phase-conductors between the bank and load-bus are known!!

Phil

 

[Ingenieur]

InJunEar...

Of course the load is unknown! But, I guarantee there is a an unbalanced 3ph, 3w, delta- or wye-load connected to the bus fed by the 3-ph bank! How can you say, the load is ignored!
You have ignored another simple, but very important fact! Power to the load can be calculated using just the info provided by the OP: 1) Source Voltage is 240V because it's a Hi-Leg connection; and 2) Line-Currents in the 3 phase-conductors between the bank and load-bus are known!!

Phil

I said he ignored the load in his calcs, not that it isn't important, it is critical
you can calculate P, but not Q, therefor not S

here's the tests
1 using his calcs assume xfmr Z is 0 (not unreasonable since <<< smaller than load Z or even conductor Z), what happens to the solution? does the matrix become indeterminent?

2 assume the xfmrs are all the same size and Z, so the xfmr Z ratios (his w and x parmeters) go to 1 and are removed from the equations
does this imply now that the circuits will be balanced since Ia + Ib + Ic =0???

 

[Phil Corso]

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

 

[Ingenieur]

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

no, you are wrong...again, multiple fronts (on the engineering and grammer, it's "you're", as in you are, not 'your', as is possessive)
what is P
what is Q
what is S

all we know for certain is |S| = V x line I per phase

V = 240 of unknown phase (can't assume 0/120/240 because we don't have any load info)
I line = 254, 296, 341 of unknown phase

you must be a real peach to work with :lol:
why so many !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! marks
like everything you say is a startling revelation or of import and profound lol

you have a bad habit of telling everyone 'they are wrong!' without EVER substantiating it

 

[Phil Corso]

InJunEar...

Reur: what is P? what is Q? what is S? I suggest, nay advise, you learn about the 2-Wattmeter method! Also, I said earlier forget 120V!

Reur comment about my being a peach to work with! You would have been much closer if you had mentioned "meatball"!

Regarding "substantiating it"! Read some of my earlier contributions. You will note I often offered free XCEL solutions! In fact I advised a METHODOLOGY to use for this problem!

Phil

 

[Ingenieur]

InJunEar...

Reur: what is P? what is Q? what is S? I suggest, nay advise, you learn about the 2-Wattmeter method! Also, I said earlier forget 120V!

Reur comment about my being a peach to work with! You would have been much closer if you had mentioned "meatball"!

Regarding "substantiating it"! Read some of my earlier contributions. You will note I often offered free XCEL solutions! In fact I advised a METHODOLOGY to use for this problem!

Phil

Numerical values will suffice (polar or rectangular your choice)
|V| 240 phase unknown
i |256/294/341| phase unknown
what is S = P + j Q ???

 

[Phil Corso]

InJunEar... I'm glad you are amenable to learning, so start with the following:

1) Given: 1-phase circuit; V= 117V @ 127 Deg; Line current = 56.3A! What is the magnitude and nature of the load?

2) Given: All of the above, but an installed Wattmeter indicates 1,812W? What is the magnitude and nature of the load?

Regards, Phil

 

[Ingenieur]

InJunEar... I'm glad you are amenable to learning, so start with the following:

1) Given: 1-phase circuit; V= 117V @ 127 Deg; Line current = 56.3A! What is the magnitude and nature of the load?

2) Given: All of the above, but an installed Wattmeter indicates 1,812W? What is the magnitude and nature of the load?

Regards, Phil

Less words, more numbers
stop answering questions with a auestion
I wish YOU were open to learning or at least proving your assertions

once again
|240| vac, phasing unknown
256/294/341 A, phasing unknown

what is S, P and Q as in S = P + jQ
very simple for a teacher of your caliber

 

[GoldDigger]

As a student I would have to say that S, P and Q are unknown. :angel:

 

[Phil Corso]

InJunEar...

I'm trying to present a solution in a manner that all (if interested) can learn as well! After all isn't that a major tenet of the MHF Forum! Thus, if you can solve a simple single-phase problem (especially for a person of your caliber, who purports to have extensive knowledge) then, we can proceed to the next step, i.e., poly-phase!

Yes, I did teach a basic Electrical-Technology course way back in the '60s! And, also taught in a Post-Secondary technical-school in the early '00s, and now in a University! But, they were and are 'second-jobs'. I am still a Power EE... 63 years, thus far... !

So, if you want to learn my way, I intentionally go slowly primarily for others on the Forum!

If you don't, then, as said in Sicilian, "Buon' vita, mia Amico!"

Phil Corso

 

[Ingenieur]

InJunEar...

I'm trying to present a solution in a manner that all (if interested) can learn as well! After all isn't that a major tenet of the MHF Forum! Thus, if you can solve a simple single-phase problem (especially for a person of your caliber, who purports to have extensive knowledge) then, we can proceed to the next step, i.e., poly-phase!

Yes, I did teach a basic Electrical-Technology course way back in the '60s! And, also taught in a Post-Secondary technical-school in the early '00s, and now in a University! But, they were and are 'second-jobs'. I am still a Power EE... 63 years, thus far... !

So, if you want to learn my way, I intentionally go slowly primarily for others on the Forum!

If you don't, then, as said in Sicilian, "Buon' vita, mia Amico!"

Phil Corso

We can learn if you show us your detailed calcs
|240| vac
Iabc 256/294/341
phasing not known
S
P
Q
???

 

[Smart $]

As a student I would have to say that S, P and Q are unknown. :angel:

Isn't S known?

It is P and Q which are not, correct?

Does it really matter regarding winding phase current?