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1. Power factor = (real power)/(apparent power)
2. No advantage of power factor.
3 Transformer is a physical device while power factor is a mathematical ratio!
When voltage and current are not in in-phase the power is not just product of RMS voltage and current.
The power factor is used to find the real power taken by the load from the well know apparent power.
Transformer is a also a reactive load which cant consume its all apparent power.
Power factor is VERY important when generating on the national grid. If the power factor is not very close to unity (real power high, reactive power low), the generators go unstable and can not control their output voltage. So all big devices connected to the national grid have a specification to keep their power factor better then .8. Also if you are running a factory with a bad power factor, you have to deal with currents much larger then required, so the gauge of the wire and size of switchgear has to be greater.
Frank
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