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

1. Aug 12, 2012

stef6987

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

2. Relevant 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;

3. 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.