What do you know about a perfect transformer ?

About the "perfect" transformer I'm sure it doesn't exists - I wish to be such devices (perfect ones), I'm not a demoralizing person, but a realistic one!

It's not perfect because its high efficiency (0.95-0.98) is at70-80% of it's maximum load; if it's used under70% it will start to "consume" reactive power which is not a good thing either. The difference between 70-80 unti100 % represents extra material which is heavy, occupy space needs to be cool down and costs extra!

If your requested power can be achieved by using two different transformers - one bigger than the other - then the bigger one will work under load, while the smaller one over loaded (it will have to carry the power rejected by the bigger one). Also not perfect and not fare!

It can be improved by using capacitors for increasing the power factor, better and much more pure alloys, but never to the perfection, since us, the creators, are not perfect!

Wish you the best! 

one that have balance resistance, infinity reading to earth between earth primary and secondary, and infinitiy reading between primary and secondary, and clean oil 

A perfect transformer , which does not exist, is supposed to be with a perfect performance =1 

 Without energy loss neither  due to the Joule effect in the windings

nor Hysterisis and Foucault current  losses in it's magnetic core.

A transformer is an electrical device that transfers energy between two or more circuits through electromagnetic induction. A varying current in the transformer's primary winding creates a varying magnetic flux in the core and a varying magnetic field impinging on the secondary winding.