I have described the condition in the transformer picture I have attached. Will the transformer still function in this condition?
Electronic – What happens if the primary and secondary side of a transformer are short circuited mistakenly
electric-machinetransformer
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kVA ratings correspond to full load conditions.
By full load is meant the load (obviously, on secondary) which would make transformer transfer it's rated power from primary to secondary. For example when 50 kVA is on full load, it would be transferring 50 kVA from primary to secondary. If primary voltage on full load is 25000 V (as in your case) then primary current should be (50*10^3 / 25000) ampere.
Now coming to your primary question,
if there isn't such currents
means that there isn't such load on secondary that can fully load transformer.
If transformer is under-loaded, primary (and hence secondary) currents would be less than full load values. For e.g. if transformer is on half-load (means load connected at secondary is half the full load), then it would drive exactly half current than full load current. Say your full load current is 'I' ampere then you half load current would be 'I/2' ampere. If transformation ration is 'k', then half-load secondary current would be 'I/2k' ampere.
If transformer is over-loaded, then it may damage winding and/or insulation. However, if we neglect such effect (and you shouldn't neglect it in practice) then, transformer which is on double-load will be drawing twice the full load current in both, primary and secondary winding.
In Australia, at least, the tap-changer is always on the HV winding. I don't recall ever seeing a transformer with the tap-changer on the LV winding.
I believe this is for economic reasons (it's cheaper or easier to build it this way). However I haven't looked this up so treat the previous statement with a grain of salt. The J&P Transformer Book, originally my Martin Heathcote, is all about the details of design, construction, and maintenance of power transformers and could probably tell you more.
To give a more concrete example, here is an example of a transformer nameplate showing the possible tap positions. (Serial numbers have been obscured to protect the innocent.)
Note that the nominal voltage ratio is 11,000 / 440 V and five taps of 2.5% are provided, two taps up and two taps down.
You say your transformer has both HV tapchanger and LV tapchanger - is this a real, physical transformer, or a theoretical transformer? Having both HV and LV tap changer would be an extra expense and I am not sure if there would be any advantage to providing both.
A quick skim of J&P Transformer Book (12e) ยง2.4 mentions that HV tap-changers imply operation at "constant flux density", while LV tap-changers imply operation at "variable flux density".
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Best Answer
If the primary and secondary turns are identical (i.e. a 1:1 turns ratio) then the transformer will continue to function but of course it won't isolate any more because you've bypassed the isolation.
Consider taking two long wires and wrapping them round a transformer core many times. As a pair they can be shorted together at the ends and this just forms a single winding. If they are open circuited the AC on one winding produces exactly the same AC voltage on the other and so clearly they can be connected together as per your diagram.
Any other turns ratio and the thing will smoke.