# Balanced three phase circuit Y-Y with neutral

Here is my equivalent balanced three phase circuit Y-Y with neutral:

Rla + jXla is my line impedance by phase. L1 and L2 are my loads. The exercise is saying that L1 absorbs 180 W and 240 VAr, L2 absorbs 600 VAr and has 0.6 lagging power factor. The line impedance is 5 + j8. The line voltage is 240 V. Its asking me what is the voltage VAN across the loads.

LOOK WHAT I HAVE TRIED:

VAN.IL1* = SL1 = 180 + j240 VA
VAN.IL2* = SL2 = 450 + j600 VA
VAN.IL* = SL = SL1 + SL2 = 630 + j840 VA
IL = IL1 + IL2
VaA = IL.(Ra+jXLa)
VAN = Van - VaA
Van = 240/sqrt(3) with angle of -30 degrees
SL/IL* = Van - IL.(Ra+jXLa)
(630 + j840)/IL* = (120 - j69.282) - IL(5 + j8)


When I throw this equation at wolfram alpha, It says there's no solution:

• I don't have time to go through this fully, but the Alpha analysis says there is no solution assuming $z>0$*(i.e. $z$ is real). It doesn't actually say there is no solution. You're looking for complex solutions Feb 26, 2014 at 21:56