What the capacitor Current formula?, For 1 KVAr how amps
its required? for using the KVAr for boosting the PF Design
Calculation.( Eg: for 30 KVAr required how many KW?)

For correcting PF KVAr is introduced, thus formula

pf=cos A is significant

there you should have a desired PF. If for example you need
a power factor of .90 to maintain for a 30kVAR the watts
that would come will be:

A=arccos .90
A= 25.84

WATTs= KVAR/tan 25.84

= 62500 watts approx.

remember that for PF correnction it is the KVAR that is in
need of computation and not the watts so the question would
rather be, how much capacitor kVAR you need to correct the
power factor.

The question requires more details.
First the "K" represents kilo or 1000.
The real power (kW) can be thought of as the x-axis and the
reactive power (kVar) from inductance or capacitance can be
thought of as the y-axis. The hypotenuse is the
Apparent power (KVA). The relationship of Real to apparent
power gives the Power Factor, where a power factor of 1.0
simply means that you only have real power, no reactive
power. The leading and lagging VARs from capacitance and
inductance, respectively can be added numerically since
they are on the same axis.
To ask, how muck kVars are required for a given kW doesn’t
make a lot of sense because you need to include the desired
power factor.

How a synchronous generator practically work? what is the
function of avr(automatic voltage regulator)in synchronous
generator?how the connection of avr to the generator made
practically?please give me the answer.