# Homework Help: Three-phase power factor correction

1. Jan 25, 2016

### Frank-95

Hello. I have a doubt regarding the following problem:

1. The problem statement, all variables and given/known data

Calculate capacitors' capacity to rephase (cos(φF) = 1) the load ZL

2. Relevant equations

The formula to calculate capacity in this case is:

CY = P(tan(φi) - tan(φF))/ωVrms2

or

CΔ = P(tan(φi) - tan(φF))/3ωVrms2

3. The attempt at a solution

ZLY = ZLΔ / 3 = 9 + 12 j Ω = 15e53,13j

The load phase is then 53,13. The final phase must be cos(φF) = 1 -> φF = 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 :)

2. Jan 25, 2016

### 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 cancelled 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 Xc. Given the frequency, you can find C from it.
This is a way of pf improvement in a power system.

Last edited: Jan 25, 2016
3. Jan 25, 2016

### Frank-95

Thanks I did it this way :)