Simple power factor correction calculation:
Motor input = P = 5 kW
Original P.F = Cosθ1 = 0.75
Final P.F = Cosθ2 = 0.90
θ1 = Cos-1 = (0.75) = 41°.41; Tan θ1 = Tan (41°.41) = 0.8819
θ2 = Cos-1 = (0.90) = 25°.84; Tan θ2 = Tan (25°.50) = 0.4843
Required Capacitor kVAR to improve P.F from 0.75 to 0.90
Required Capacitor kVAR = P (Tan θ1 – Tan θ2)
= 5kW (0.8819 – 0.4843)
= 1.99 kVAR
And Rating of Capacitors connected in each Phase
* = 0.663 kVAR
If you know overall plant kW and you want to raise the power factor to 0.99, then you should know what is power factor of supply power available to you. That you can calculate if you know KVA rating of supply transformer and total KW of your plant loads. Divide KW by KVA to get cos theta = power factor.
If transformer is 1000KVA and your plant loads sum to 800kW, then your supply will have a power factor of 0.8. For changing starting power factor of motor from 0.2 to Unity power factor, the kVAR will be around 5 times the kW rating of the motor. So big but exists online only for few seconds giving needed high starting torque.
For changing motor standard power factor of 0.8 to unity, you will need kVAR about 75% of kW rating of motor. To change from 0.75 to 0.9, kVAR around 35 % of kW rating required.