Impedance of three 3ph transformers in parallel

[Spy613]

I am working on a short circuit calculation for three 3ph 75kVA transformers in parallel. All three are identical with 1.9%Z.

The total bank rating is then 3x75kva = 225kVA. But I'm not sure on the equivalent impedance? Would it be 1/ZT = 1/z1 + 1/z2 + 1/z3 (Where z1/2/3 all equal 1.9%) which would give an equivalent of a 3ph 225kVA transformer with Z=0.6333%?

If the transformers were three 1ph all with 1.9%Z, then as I understand it the total equivalent would also be a single 3ph 75kVA with Z=1.9% correct?

Thank you!


These are my numbers so far below... but I'm not sure on the Z which effects everything else downstream.
--------------------------------------------------------------------------------
Line-to-Line (L-L) Fault
Fault X/1

I/FL =
=3 x 75kVA x 1000 = 216.51 A
600 x 1.732

Multiplier =
= 100
1.9% x 0.9*

= 58.48

 

[waross]

First convert the % impedance to the same base.
Yours are already the same impedance.
3 x 75 KVA = 225 KVA.
PU impedance is 1.9 on a base of 225 KVA.
The impedance in Ohms is 1/3 of the original impedance.

Additional information.
Paralleling transformers of different PU impedances is not a good idea.
The capacity of the parallel combination may be less than the capacity of the largest transformer.
Transformers with equal impedances will share a load in proportion to their ratings. Hence a 100 KVA transformer will share a load with a 10 KVA transformer if their impedances are equal.
BUT
Consider a 100 KVA transformer with an impedance of 3.8%. It is desired to pair this with a 10 KVA transformer with an impedance of 1.9%.
The 100 KVA transformer must be converted to a 1.9% imp base.
Rated at 50 KVA the impedance will be 1.9%.
Paired with a 10 KVA transformer at 1.9% imp, the 10 KVA transformer will be fully loaded when the 100 KVA transformer is 50% loaded.
By paralleling this combination, we have reduced the capacity from 100 KVA to 60 KVA.
On the other hand, it is safe to parallel if the larger transformer has the lower % imp, but when the larger transformer is fully loaded the smaller transformer will be less than fully loaded.
Different X:R ratios add a little complication.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[Spy613]

Excellent thank you for your reply. Glad to hear I was on the right track. And thanks for the additional information with regards to different transformers.

Just to confirms, it’s a third because of this formula. 1/ZT = 1/z1 + 1/z2 + 1/z3 (Where z1/2/3 all equal 1.9%) which would give an equivalent impedance of Z=0.6333%. Which is also a 1/3 of the original 1.9%.

This would give me a multiplier for short circuit calcs of 100/0.6333 = 157.9, which seems very large but everything seems to make sense now.

 

[waross]

The Ohmic impedance of the three transformers is 1/3 of the Ohmic impedance of one transformer.
The PU impedance is still 1.9% but now on a base of 225 KVA rather than a base of 75 KVA.
Using 1/3 of the Ohmic impedance of one transformer should give the same result as using the same % imp (1.9%) on a base of 225 KVA.
Don't mix Ohmic calcs with % impedance calcs.
I think that you have it now.

Counter-intuitively,
Paralleling transformers with equal % impedance but differing X:R ratios will result in the sum of the individual transformer KVAs being slightly greater than the load KVA.
Hint: The Phase angles of the transformers will be slightly different from each other and from the load.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[Spy613]

Ok, That confused me now a little bit.

So to perform my short circuit calculations I’m trying to do, I am trying to first get the equivalent transformer for the bank of three.

So the three 3ph 75kva would then equal one 225kva with a 0.6333%z or a 1.9%Z impedance?

 

[waross]

So the three 3ph 75kva would then equal one 225kva with a 1.9%Z impedance on a base of 225 KVA.
At the end of the calculations, the Available Short Circuit Current of three 75 KVA transformers in parallel should be three times the ASSC of one 75 KVA transformer.


Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[waross]

So the three 3ph 75kva would then equal one 225kva with a 1.9%Z impedance on a base of 225 KVA.
At the end of the calculations, the Available Short Circuit Current of three 75 KVA transformers in parallel should be three times the ASSC of one 75 KVA transformer.


Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[Spy613]

Ok great thank you it’s starting to make sense. So the equivalent transformer is a 225kva 1.9%z.

But now I just don’t understand how three of these transformers in parallel have the same impedance as a single transformer? To me a single equivalent impedance of 0.6333 makes sense?

But if the total ASSC is three times a single one, then I see using the equations that 1.9%z makes sense, I just don’t understand why that number stays the same?

Thank you

 

[waross]

75 KVA at 240 Volts = 312.5 Amps
312.5 Amps / 1.9% = 16447 Amps ASCC (Available Short Circuit Current)

225 KVA at 240 Volts = 937.5 Amps
937.5 Amps / 1.9% = 49,342 Amps ASCC

16447 Amps ASCC x 3 = 49,342 Amps ASCC



Bill
--------------------
"Why not the best?"
Jimmy Carter