How Do You Calculate Current in a Three-Phase System's Middle Capacitor?

[Frank-95]

Homework Statement

In the following three phase system, calculate the current in the middle capacitor:

Homework Equations

I = V/Z

Z_Y = Z_Δ / 3

The Attempt at a Solution

Hello! I'm trying to figure out a method for solving any generic three phase system. In particular, I found very effective method the single phase analysis, by reducing generators and loads to star loads (if they are originally delta loads). I don't know if this can always be done, and I have some doubts about parallel loads.

As regards this particular system, I converted the delta load to a star load, so:

R_2Y = R_2Δ / 3

Capacitors are already disposed in a star load. So I consider the following single phase system:

(R2 and R1 are switched here, I apologise)

Is that the right equivalent single phase system?
If this is right, I would just need to calculate equivalent impedance, find the first phase current, and add -120° to find the middle one right?

If that is not right, where I mistakened? Thanks :)

 

[KataKoniK]

Hello there! Your approach for solving this three phase system is correct. Converting the delta load to a star load is a valid method and it can always be done. As for the parallel loads, you can use the formula ZY = ZΔ / 3 to convert them to a star load as well.

In the single phase system, you can calculate the equivalent impedance using the formula Z = √(R^2 + (Xc - Xl)^2) where R is the resistance and Xc and Xl are the capacitive and inductive reactance respectively. Once you have the equivalent impedance, you can use the formula I = V/Z to calculate the current in the first phase. To find the current in the middle capacitor, you can use the formula I = I1 * e^(-j120°) where I1 is the current in the first phase and j is the imaginary unit.

Overall, your approach is correct and you just need to make sure to use the correct formulas and values to calculate the current in the middle capacitor. I hope this helps! Let me know if you have any further questions. Good luck!