cuky2000 website?

[PowerWolve]

Hi cuky2000, the work you have posted on the boards is phenomenal, and have referenced it a lot over the years. It's been a while since I've gone looking, but I believe your website has been down for a while now. Do you have a replacement for this by chance, with your various resources posted?

Thanks in advance!

 

[electricpete]

Cuky seems to have not logged in since January.

https://www.eng-tips.com/userinfo.cfm?member=cuky2000

But maybe someone will bring this to his attention or know his website.

 

[waross]

This is for discussion only. Not a real world problem, at least not for me.
Looking on the web for cuky2000 I came across this interesting and unsolvable problem.

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?

My Answer:
Why is this not solvable?
First consider the load sharing of single phase transformers in parallel.
Transformer loading is considered in KVA, not kW.
We have Amps and Volts but no PF, thus KVA.
Loads will be considered as KVA loads.
When two transformers of equal KVA are connected in parallel they will share loads in the inverse ratio of their respective PU impedance voltages.
If the transformers are unequal, the greater KVA rated transformers are normalized to the lowest KVA.
eg; A 50 KVA transformer is paralleled with a 100 KVA transformer at 5% imp. Volts.
The 100 KVA transformer is considered as a 50 KVA transformer at 2.5% imp. Volts.
Note that PU impedance voltages are not given
With 341 Amps on one line it is possible that either the 75 KVA or the adjacent 50 KVA transformer is overloaded, but this can not be proven with the information given.

Now look at a single phase load on a delta transformer bank.
With equal transformers a delta bank may be considered as a single transformer in parallel with an open delta.
An open delta may be considered as a single transformer with the same characteristics
That may sound counter intuitive, but if you calculate a single phase load on an open delta, you will see that the voltage drops under load and the effective PU imp volts are equal to the single transformer that was removed to form the open delta.
The factor that is at first is overlooked is that the current will be at 50% lagging on one transformer and at 50% leading on the other transformer.
So any load current on one phase will be shared by all three transformers.
It is not a safe assumption that the normalized impedance voltages of all three transformers is equal and so sharing will not be equal.
It is a reasonable assumption that the 75 KVA transformer will take a greater share of the load, but not provable.

but I need to know how to calculate it

You can't without knowing the transformer impedances.
Suggestion:
Send the lineman out to measure the X1 current of each transformer and to record the rated %imp volts of each transformer.
You will know the answer, and you will be able to double check your calculations.

Some seat of the pants engineering based on experience.
I see this transformer connection most often for a mix of motor loads and single phase (mostly lighting) loads.
Take the average of 256 A and 294 A = 275 Amps. The loads are probably equal, but with motor loads, a small primary voltage unbalance will cause this current unbalance.
275 A x 1.74 x 240 V / 1000 = 114 KVA. Three phase load.
(341 A - 275A) x 240 V / 1000 = 16 KVA. Single phase load.
114 KVA / 3 = 38 KVA per transformer.
Double check;
275 A / 1.73 x 240 V = 38.1 KVA three phase load.
With a 114 KVA three phase load, and reasonable impedances, this bank should be able to support a 16 KVA single phase load.

Doubts:
With 16 KVA single phase load, we would expect the currents on both sides of the transformer carrying the most load to be high.
Those currents are possible but in reality are highly suspect.

--------------------
Ohm's law
Not just a good idea;
It's the LAW!