Some general concepts about using transformers at lower voltage than rated:
The magnetic flux density in the core will be proportionally lower, and for this
reason the power loss in the core will be much lower. That's a good thing. But
the good things end there!
The transformer has a certain current rating. This rating essentially remains in
place even while operating at a lower voltage. This means that the output power
is reduced proportionally to the voltage reduction. You might get away with
drawing SLIGHTLY more current, thanks to having less core loss and thus less
overall heating. But given that the core loss and wire loss happen at different
places, and that the wire loss grows with the square of the current, any
increase in the current you could draw is almost negligible.
The transformer has a certain resistance, and a certain leakage inductance.
These cause a certain voltage drop at full current. This voltage drop remains
the same when the transformer operates at lower voltage. As a result, the
percentual voltage drop grows when you operate the transformer at lower voltage.
In other words, regulation suffers.
The above effect also increases the percentual power loss relative to output
power, reducing the overall efficiency of the transformer.
Despite all the above, you CAN of course use a transformer at reduced voltage,
as long as you are willing to accept that this transformer is larger, heavier,
less efficient, more lossy, and has worse regulation, than a transformer
designed for the exact working conditions. The only aspect that will be better
than with an optimized transformer is the core loss, and this means that at zero
load (RX) the transformer will run cooler than the optimized one.
Now if you plan to provide the reduced input voltage by means of a VARIAC, you
have to add its bulk, weight, cost, power loss, and further regulation loss into
the equation. At that point it hardly makes sense, except for purely
experimental purposes.
It is _not_ a problem to run a transformer in reverse. The roles of primary and
secondary can be interchanged without penalty, as long as each of them is for
the same power level, which is the case with pole pigs. Instead a transformer
having one primary, and several secondaries of different voltage and current
ratings, cannot be reversed very well, because none of the secondaries is rated
for the full power.
It usually doesn't matter a lot which winding goes first, primary or secondary.
Practical winding considerations are more important: If one of the windings
needs a very thick and stiff wire, this winding is usually wound last, because
then the bending radius required for the big wire is larger. In very high
voltage transformers, insulation requirements often dictate how the windings are
arranged. And in transformers requiring extremely low leakage inductance, it's
common to intersperse the primary and secondary.
Manfred
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