Question:

Motor Connected Load = 811kVA

Motor PF = 0.883

Capacitor size = 7000 kVAR, PF = 0

Using the equation P = S*PF:

Pmotor = Smotor*PFmotor = 811 * 0.883 = 716.11 kW

Pcapacitor = 0

Ptotal = Pmotor + Pcapacitor = 716.11 kW

Using the equation Q = S*sin(acos(PF))

Qmotor = Smotor*sin(acos(PFmotor)) = 811*sin(acos(0.883)) = 380.66 kVAR

Qcapacitor = Scapacitor*sin(acos(PFcapacitor)) = 7000*sin(acos(0)) = 7000 kVAR

Qtotal = Qmotor - Qcapacitor = -6619.34 kVAR

Stotal = sqrt (Ptotal^2 + Qtotal^2) = 6658 kVA

Calculating PF:

PF = Ptotal / Stotal = 716.11 / 6658 = 0.1076 --> 10.76%

Without the capacitor, Stotal = Smotor, thus PF = PF motor = 0.883 --> 88.3%