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What size of capacitor can bring the power factor to 0.90 lagging, then what will be the real power?

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- Thread starter phillies09
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What size of capacitor can bring the power factor to 0.90 lagging, then what will be the real power?

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Would anyone please verify my approach is correct?

Initial 3 phase load of Ptotal =520kW, Pf1=0.85, and Vline=31540volts

3*Pf=Ptotal

Pf=520kW/3=173.33kW

For grounded wye,

Vf=Vline/SQRT3=18209volts

Pf1=0.85,

Pf1=Sf1 * (cosf1), where Sf1= Pf1/(cosf1)

Sf1=173.33W/0.85=203.92kVA

Qf1=SQRT(Sf12-Pf12)=107kVAR

Pf2=0.96,

Sf2=Pf2/(cosf2) = 173.33kW/0.96=180.55kVA

Qf2=SQRT(Sf22-Pf22)=50.54kVAR

Xf(reactive) = Vf2/Qf=182092/Qf=331.567E6/ Qf

Xf(before) = 331.567E6/107k=3086Ω

Qfcap= Qf1-Qf1=107k-50.54k=56460VAR

Xfcap= Vfcap2/Qfcap= 331.567E6/56460= 5872 Ω

a) The size of the capacitor per phase C is defined as

C=1/(2*p*f* Xfcap)=1/(376.99*5872)=0.416mF since it is assumed f=60Hz

b) Real power should remain same since we are not changing anything about the resistance part of the impedance so

Ptotal = 3* Pf =520kW

Pf=173.33kW per phase

C) Qtotal = 3*Qf

So Qtotal before = 3*107kVAR=321kVAR and Qtotal after = 3*50.54kVAR=151.62kVAR

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