Optimized Autotransformer Rating - 2kVA to 4kVA?

[jaus tail]

Homework Statement

A single-phase, 2 kVA, 100/200 V transformer is reconnected as an auto-transformer such that its kVA rating is maximum. What is the new rating in kVA?

Homework Equations

Rating is KV times the current.

The Attempt at a Solution

For single winding transformer:
O/P voltage is Vab = Vac - Vbc.
Vab is 200 V as this is given in question.
O/P current is 2KVA/200 is 10A.

For auto transformer:
O/P voltage is Vac
Vac is Vab + Vbc is 200 + 100 is 300V.

O/P current is same in both cases that is flowing through the load and it is 10A.
So KVA of auto transformer is 300 * 10 equals 3KVA.

But books goes through other method where Vac is 200V
So Vab is 200 - 100 = 100 V.
KVA auto / KVA single phase = Vac/(Vac - Vbc) = 1/(1-Vbc/Vac) = 1/(1-0.5) = 2.
So KVA auto is 2 * KVA single phase = 2*2 = 4KVA.

Which method to use and why? Why is o/p voltage 200V in case of auto? Shouldn't it be 200 + 100 as I've drawn in picture?

 

[cnh1995]

I also don't understand your book's method and I am getting an answer which is more than the answer provided by the book.

In the diagram you've posted, is Vab=200V already given or are you assuming it?
Try Vbc=200V i.e. the HV winding is supplied with 200V and HV+LV is the output.

 

[jaus tail]

No, I am assuming Vab = 200V. In the question it says it's a 100/200V transformer, so I'm assuming it means there is a 100V input suppy.
Thus for whatever connection, single winding or auto transformer the input volts should be 100V, right?

I'm sorry, the book doesn't give any solution. I had written that answer from the derivation in the book of single winding to auto transformer formula.

***

If I connect 200 V to HV. Then... Vbc = 200V. Vac = 200 + 100 = 300V.
Now Vab = 100V. And it's a 2kva, so I ab = 2000/100 = 20A.

This Iab is same current through load for auto transformer so KVA of auto = 300 * 20 = 6000. 6 KVA.

But how can I connect 200 V to HV? Shouldn't it be only 100 V to HV, as the single winding transformer is 100/200 V.

 

[cnh1995]

as the single winding transformer is 100/200 V.

Doesn't that mean HV is at 200V?

so KVA of auto = 300 * 20 = 6000. 6 KVA.

Yes, assuming proper winding polarity. If the windings are connected in series-aiding fashion, the autotransformer rating will be 2kVA. So the windings should be connected in series opposition.

 

[jaus tail]

Doesn't that mean HV is at 200V?
Oh. I thought it means that I have only 100V supply as input and I can connect it to LV side. Cause if I connect 100V to HV side then i'll get 50V.

Yes, assuming proper winding polarity. If the windings are connected in series-aiding fashion, the autotransformer rating will be 2kVA. So the windings should be connected in series opposition.

We haven't cleared this topic yet. In the diagram that I have drawn, is it series aiding or opposition?

 

[cnh1995]

You can connect 200V on the HV side (making it the primary) and get 300V on the autotransformer secondary.

We haven't cleared this topic yet. In the diagram that I have drawn, is it series aiding or opposition?

It can't be said because the dot convention is not used in the diagram. But don't think about that for now. I believe the connection is assumed to be in series-opposition fashion if not mentioned.

 

[NascentOxygen]

But how can I connect 200 V to HV? Shouldn't it be only 100 V to HV, as the single winding transformer is 100/200 V.

My reading of this is that the parameters to work with are a supply of 100V, and the thin-wire winding rated to carry 10A.

Though, admittedly, it does not rule out the transformer being powered by 200V, so perhaps that should be examined to see whether it endows the transformer with a higher KVA rating.