Question

Three balanced three-phase loads are connected in parallel. Load 1 is Y-connected with an impedance of 400+j300 2/0; load 2 is A-connected with an impedance of 2400-j18000/0; and load 3 is 172.8+j2203.2 kVA. The loads are fed from a distribution line with an impedance of 2+j16 0/0. The magnitude of the line-to-neutral voltage at the load end of the line is 2413 kV. Calculate the total complex power at the sending end of the line. :) Magnitude of the total complex power in kVA: .) Phase angle of the total complex power in degrees:

Answer 1

Given, Receivingend all the three-loads parallel Load-1 => Y- Connected with 400+ j300 22/phase Load-2 => 4- connected with 2400 - 11800 2/phase Load-3 > power of 172.8 +32203.2 kVA line to neutral voltage @ Load end = 2413 kV MeNl = 2413 KV distribution limpe impedance 2+11612 |phase Single- line diagram Sendingend 2+316-02 load- Load -2 Iload 3 VR 24V3kV (L-N) Load-1 power capparent) of 3-phase power of Load-1 Jacovsky Ivod Vph VIN 400+1300 =ph 7 400+1300 = 3x single-phase power 4007300

Single- phase power Vph. Iph Iph* Vph. [Vph Zph Vph. Vph [..Q.am 1014] Zph = IVphp? Zph* .: total apparent power of Load -1 is 2 3x IVphi? Eph* 3x/2418x10° (400+13007* 3x(2418x103) 400-1300 10368_36.86° KVA 8294.4+ 6220.80 KVA load-1 KVA Load-2- [vph=VL-2 Zph = 2400 - 18000 1

Simibaly Load-2 apparent power (3-phase) 3x IVph/? Eph* = 3x { VELI? 3x / VEx Venta (24007 18001)* 2400 +TRO = 3x [13x 2448 X10012 2400+ 18001 = 5184 2-36.86° KVA 41-47.2-3110.43 kVA .: load-2 KVA given, load-3 kVA = (3-phase) 172.8+32203.2 kVA .: total KVA (3 phase) @ Receiving end = load-Ikva + Lood-2xvA+200d-3k (3-0) (3-0) = 12614.4 +5313.63 kVA Receiving end kVA = 12614.4 + 5313.64 kVA = SR noces, Receiving end ccorrent (IR) =? we know that V3 x IV. Rec. * (IR) ISRI =) Vax Vax IV.N/ Reca x TIR) = 1 SRI 3x 2473x@IR) = 13 687 KVA > TR1 = 13687x103 3x24V3x103 (IR l = 109.75 A

582.66_82-87° KVA total- noco, Bending end kVA Receiving end kVA +, power- loss in the line total pocos losa total power loss in the line 3x |IR|2x Zline = 3x (Single-phase power loss) 3x (109.75) ?x (+16-2) Hlotal Powel loss in line = 72.27 +1578.163 kVA Sending end kVA - 12614.4+ 15313.6+ 72.27+ 3578163 Sending end kVA 13988 L24.91 KVA magnitude of sending end complex power = 13988 kVA thase angle of Sending end compler power = 24.91°