the transformer Volume law:

Not widely known - the volume of a transformer ( i.e. cm^3 ) gives us a proportional idea of the power it can process -

So if a transformer 4cm x 4cm x 4cm ( 64cm^3 ) and can process 2kW say - with a 40 deg C rise, then,

if we increase the dimensions by 4cm on each side ( now 512cm^3 ),

the resultant transformer ( same frequency ) can process 16 kW,

i.e. Eight times more !

even though it's only twice as wide, twice as tall, twice as long.

There is a caveat here though - and that is the surface area to volume ratio of the smaller 2kW transformer ( 150% ) is noticeably larger than for the 16 kW transformer ( 75% ) - so you win out on cooling for the smaller transformer for convection or fan assisted cooling approach.

Thus your cooling methods must change for larger and larger transformers, as their surface area shrinks compared to their volume and power processed.

This is why the planar transformer has enjoyed a revival in the last 10-15 years in the 2kW to 20kW bracket. Alongside advances in copper stampings, interconnects and insulation systems, pcb windings and similar - the fact that you can cool the planar transformer on 2 sides provides a huge advantage over simple convection or fan assisted cooling.

The remaining issue is to get the heat from the windings to the core - and then through the relatively thin cores into the heatsinks for eventual ( usually ) forced air cooling - advances in potting materials ( thermally conductive ) assist greatly with that.

Another approach is to split your power transformer into 2 or 3 parts,

this gives far more surface area for cooling - and may well be a cost saver - as you can use more common, smaller parts to create the transformers in a high volume way.

Planar's have the draw back of larger physical footprint - and often increased capacitances with windings and pri to sec - so choice of topology is key to getting the most out of them.

The designer has choices - recognising the fundamentals helps make good ones

for more - go to pwrtrnx.com