Determining total power in a 3 phase system and star capacitance?

[stef6987]

Homework Statement

A 415V, 50 Hz three phase supply supplies three balanced loads which draw a total
apparent power (S) of 38 kVA at a power factor of 0.78 lagging. The three loads are
as follows:
LOAD 1 (STAR): 10.6 kVA at a power factor of 0.57 lagging;
LOAD 2 (DELTA): 20 kW at a power factor of 0.53 lagging;
LOAD 3 (DELTA): ZRW = ZWB = ZBR (Balanced unknown)

Homework Equations

(i) the STAR capacitance in both kVAr and microfarads to correct
the over all supply Power Factor to 0.85 lagging.
(ii) The total line current drawn from the three phase supply before
and after power factor correction;

The Attempt at a Solution

For (i) - Because the total PF is changed, this means the over VAR and W have changed
This is my attempt. The line voltage of the generator is 415V, which in star phase is ~240V
I can use Scos(θ) and Ssin(θ) with the PF of 0.85 to find the new Q and P. Now i have all the values to calculate the total line current, and hence Phase current of the STAR load... I'm not really sure where to go from here :\

for (ii) I suppose this is pretty straight forward, using the two different PF's i can calculate two different values for total line current.

Am i going about this the right way?

 

[KataKoniK]

Any help would be greatly appreciated!

Hello,

Your approach for part (i) is correct. To find the necessary capacitance in both kVAr and microfarads, you need to first calculate the new values for reactive power (Q) and active power (P) using the new power factor of 0.85. These can be calculated using the equations S = √(P^2 + Q^2) and tan(θ) = Q/P, where θ is the phase angle of the load. Once you have the new values for Q and P, you can use the equation Q = -P tan(θ) to find the necessary capacitance in kVAr. To convert this to microfarads, you can use the equation C = Q/(ωV^2), where ω is the angular frequency (2πf) and V is the line voltage (415V in this case).

For part (ii), you can use the total power formula, P = √3VLILcos(θ), to calculate the total line current before and after power factor correction. Once you have these values, you can use Ohm's law, I = V/R, to find the phase current for each load.

Hope this helps! Let me know if you have any further questions.