Three-phase power factor correction

[Frank-95]

Hello. I have a doubt regarding the following problem:

1. Homework Statement

Calculate capacitors' capacity to rephase (cos(φ_F) = 1) the load Z_L

Homework Equations

The formula to calculate capacity in this case is:

C_Y = P(tan(φ_i) - tan(φ_F))/ωV_rms²

or

C_Δ = P(tan(φ_i) - tan(φ_F))/3ωV_rms²

The Attempt at a Solution

Firstly I converted the delta load in a star load:

Z_LY = Z_LΔ / 3 = 9 + 12 j Ω = 15e^53,13j

The load phase is then 53,13. The final phase must be cos(φ_F) = 1 -> φ_F = 0.
In the image I posted I made an error: the pulsation isn't 50 Hz, the frequency is; hence pulsation ω = 100 π Hz.

Now I have initial and final phase, pulsation and I should apply the formula for finding capacitor, but the problem voluntarly do not give source voltages, so my doubt is: should I leave capacity dependent from power and root mean square voltage, or am I not considering something and I can make some more calculation? Thanks :)

 

[cnh1995]

I believe you don't need to convert delta to star here. To make the pf unity, the circuit must be seen as purely resistive by the source. So, inductive reactance per phase must be canceled out by capacitive reactance per phase, connected in parallel. I think you should just calculate the equivalent impedance per phase and equate it's imaginary part to 0.You will get X_c. Given the frequency, you can find C from it.
This is a way of pf improvement in a power system.

 

[Frank-95]

Thanks I did it this way :)