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is it possible for a transformer to get maximum efficiency when working under more than the rated load with the same power factor...?
No! More than rated load means more current and more Copper Loss; thus, the efficiency would only reduce.
sir one more question....if the transformer operating under more than the rated load with a power factor{example: 0.8leading} more then the rated load power factor{example:0.6lagging} is it the situation to get....maximum efficincey ?
Before you go any further down this path....Don't!
Go back to your text book and research how Transformers work, their limitation and understand what "Rated Capacity" actually means.
Leading Power Factor is detrimental to transformer performance and NOT free energy.
Regards, Sapper
p.s. running ANY piece of equipment beyond its rated capacity is detrimental to its operational life
Leading or lagging PF will be detrimental to transformer efficiency.
For goodness sake get an engineer to look at the scenario, because clearly you haven't a clue.