Condition for parallel AC Mains power transformer operation

[jaus tail]

Homework Statement

Homework Equations

I think both A and C are right answers.

The Attempt at a Solution

1 condition is pu Z(leakage) must be same on respective KVA rating for load sharing.

Now: Zpu = Z(actual)/Z(base) ----equation 1
For Zpu of both transformers to be same, the right side of above equation must be same.
Z(base) is inversely proportional to KVA rating of transformer. -----point 2
Voltage ratio of both transformers is same. This is also condition for parallel operation.
So Zpu is directly proportional to Z(actual) times KVA rating -----from 1 and 2

And since Zpu is same for both transformers on respective base, it means: the right side of equation 1 is also equal for both transformers.
Thus Z(actual) times KVA rating is same for both transformer.
Which means the Z(actual) and KVA rating are inversely proportional (Product is same)
But book has only given C as right answer.
Why is A incorrect?

 

[NascentOxygen]

Is leakage impedance exactly the same as leakage reactance?

 

[jaus tail]

Oh yeah. Leakage impedance is leakage reactance (from the flux that doesn't link with both windings) + resistance of winding.
So then A should be right answer. But book has given C has right answer?

Also I checked here:
Test Book Gate Questions:
https://testbook.com/gate-ee-practice/core/electrical-machines-55d3738f2a396532e8890e0b/55b6176bec7b2f64bc042620

Here also the right answer can be B, and C.
i.e Per Unit values of leakage impedance is same on respective rating
and
value of leakage impedance in ohm is inversely proportional to kva rating---> why is this wrong?

But they've said only 1st is right.

 

[NascentOxygen]

Leakage impedance is leakage reactance (from the flux that doesn't link with both windings) + resistance of winding.

Can you find a reference anywhere that says winding resistance can be considered to be the real component of something called "leakage impedance"? It would be convenient if it were so, and power engineering is noted for stretching approximations out of convenience, though I'm uneasy about renaming winding resistance as "leakage resistance". The following implies it to be so, but I'd like to have it spelled out. http://ecetutorials.com/transformer/conditions-for-parallel-operation-of-transformers/

Your option (C) uses the word "reactance" whereas the Test Book Gate Question is consistent in using "impedance" in all 3 candidate options.

Option (C) would be approximately true providing that X_s » R_s, and I think for most power transformers this might be true. Can you check on that?

 

[jaus tail]

Can you find a reference anywhere that says winding resistance can be considered to be the real component of something called "leakage impedance"? It would be convenient if it were so, and power engineering is noted for stretching approximations out of convenience, though I'm uneasy about renaming winding resistance as "leakage resistance". The following implies it to be so, but I'd like to have it spelled out. http://ecetutorials.com/transformer/conditions-for-parallel-operation-of-transformers/
View attachment 218418

My book says:
the effect of primary resistance can be accounted for by adding a voltage drop equal to I_er₁.
And a few paras later: 'x₁' is a fictitious quantity introduced to represent effects of primary leakage flux.
Total voltage drop in primary at no load = I_e (r₁ + jx₁) = I_ez₁ where z₁ is primary leakage impedance.
Your option (C) uses the word "reactance" whereas the Test Book Gate Question is consistent in using "impedance" in all 3 candidate options.

Option (C) would be approximately true providing that X_s » R_s, and I think for most power transformers this might be true. Can you check on that?

Just to be sure, in textbook Gate
https://testbook.com/gate-ee-practice/core/electrical-machines-55d3738f2a396532e8890e0b/55b6176bec7b2f64bc042620?utm_source=affiliate_cuelinks&utm_medium=non-brand&utm_campaign=CPS-Cuelinkshttps://testbook.com/gate-ee-practice/core/electrical-machines-55d3738f2a396532e8890e0b/55b6176bec7b2f64bc042620?utm_source=affiliate_cuelinks&utm_medium=non-brand&utm_campaign=CPS-Cuelinks
, the answer C should also be right, right?

The condition for parallel operation of 2 transformer:
1) same voltage rating V₁/ V₂ = same.
2) same phase angle i.e. value of X / R should be same.
3) leakage IMPEDANCE(and not only reactance) must be inversely proportional to KVA rating
OR
Leakage IMPEDANCE in p.u. value must be same on respective base
4) and same polarity. Like RYB // with RYB and not RBY

 

[NascentOxygen]

Just to be sure, in textbook Gate

, the answer C should also be right, right?

Yes, (3). Can you explain why (2) is not also correct?

The condition for parallel operation of 2 transformer:
1) same voltage rating V₁/ V₂ = same.
2) same phase angle i.e. value of X / R should be same.

(2) is not a requirement, this is explained in the final paragraph of the image I attached in post #4.

 

[jaus tail]

Yes, (3). Can you explain why (2) is not also correct?
I think (2) is also correct. There are multiple right options.

(2) is not a requirement, this is explained in the final paragraph of the image I attached in post #4.

I didn't understand. In post 4, last point, it says that phase angle must be same. So why is this not a requirement? If X/R for both transformers in parallel are different there'd be circulating current which will cause heating of winding and then temperature will rise and boom :D

 

[NascentOxygen]

I think (2) is also correct. There are multiple right options.

I thought (2) seemed correct, also.

In post 4, last point, it says that phase angle must be same.

No, it says it's okay for the phase angles to differ. So long as the magnitudes of their P.U. impedances are equal then parallelled transformers will correctly share the current in proportion to their kVA ratings. But it points out that if you do the maths, you'll see they won't be sharing the load's watts in that same proportion.

So long as the transformer's VA rating is not exceeded, they don't go Boom. Circulating current is the price you pay for improvising with two non-ideal transformers in parallel to save having to buy a new big one.