how to find capacitance for power factor improvement

 

how to find capacitance for power factor improvement

A single phase motor connected to 400 volt 50 HZ supply takes 31.9 Amp at a power factor of 0.8 lagging.

Calculate capacitance require in parallel with the motor to raise the power factor to 0.9 lagging.

 

Given Data.

Voltage:400V

Frequency:50Hz

Current:31.9 Amp

Capacitance:?

fig.1

First find the current I

Assumptions

Given power factor COSθm=0.8

Desire power factor COSΘ =0.9

Motor takes Current Im=31.9 amp

Desire current=?

fig.2

from the fig. 2

Now first calculate the Active component

ImCOSΘm=ICOSΘ

Putting the value in the above equation

31.9×0.8=I×0.9

I=31.9×0.8/0.9

I =   28.35

 

NOW FIND THE REACTIVE COMPONENTS

Im SINΘ =31.9×0.599

               =19.19

 

I SINΘ   = 28.35×0.44

                = 12.47

 

NOW FIND THE VALUE OF Ic

Ic=Im sinθ -I sinθ

=19.19-12.47

Ic=6.72

 

Now find the capacitance value

Ic=V/Xc

  =V/(1/2×3.14×50×C)

6.72 =400×2×3.14×50×C

C=400×2×3.14×50/6.72

C=53.50 microfarad