In a balanced Y-? circuit shown below, the magnitude of the phase voltage is VP = 635V (rms). The phase impedance of the load is Z? = 66 + j39 ? per phase. The wire impedance is ZW = 11 + j16 per wire. Find line current and phase current assuming ?Van = 0o.
ZY = Z?/3 = 22 + j13 = 25.5539?30.5792o ?
Zt = ZW + ZY = 33 + j29
Van = 635?0o V, Vbn = 635?-120o V, Vcn = 635?120o V
IA = Van/Zt = 14.4542?-41.3086o A
IB = Vbn/Zt = 14.4542?-161.3086o A
IC = Vcn/Zt = 14.4542?78.6914o A
VA = Van - ZW×IA = 369.3615?-10.7294o V
VB = Vbn - ZW×IB = 369.3615?-130.7294o V
VC = Vcn - ZW×IC = 369.3615?109.2706o V
VAB = VA - VB = 639.7529?19.2706o V
VBC = VB - VC = 639.7529?-100.7294o V
VCA = VC - VA = 639.7529?139.2706o V
IAB = VAB/Z? = 8.3452?-11.3086o A
IBC = VBC/Z? = 8.3452?-131.3086o A
ICA = VCA/Z? = 8.3452?108.6914o A
Vp=635;ZD=66+39j;Zw=11+16j;
ZDp=R2P(ZD)
theta=ZDp(3)
thetad=ZDp(2)
ZY=ZD/3
ZYp=R2P(ZY)
Zt=Zw+ZY
Van=P2Rd(Vp,0)
Vanp=R2P(Van)
Vbn=P2Rd(Vp,-120)
Vbnp=R2P(Vbn)
Vcn=P2Rd(Vp,-240)
Vcnp=R2P(Vcn)
IA=Van/Zt
IAp=R2P(IA)
IB=Vbn/Zt
IBp=R2P(IB)
IC=Vcn/Zt
ICp=R2P(IC)
VA=Van-Zw*IA
VAp=R2P(VA)
VB=Vbn-Zw*IB
VBp=R2P(VB)
VC=Vcn-Zw*IC
VCp=R2P(VC)
VAB=VA-VB
VABp=R2P(VAB)
VBC=VB-VC
VBCp=R2P(VBC)
VCA=VC-VA
VCAp=R2P(VCA)
IAB=VAB/ZD
IABp=R2P(IAB)
IBC=VBC/ZD
IBCp=R2P(IBC)
ICA=VCA/ZD
ICAp=R2P(ICA)
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