Tutorial on Power Flow Through A Short Transmission Line
Question 1
Two single-phase ideal voltage sources are connected by a line of impedance of 0.7+j2.4 Ω
as shown in Fig 1. Vs = 500  16.26◦ V and VR = 585  0◦ V.
(a) Find PS, QS, PR, QR and determine whether they are delivering or receiving real and
reactive power.
(b) Also, find the real and the reactive power loss in the line.
Ans: (a) PS = 28000 W, QS = -21000 Var, PR = -24570 W, QR = 32760 Var. From the results,
since PS is positive and PR is negative, source at the sending end generates 28 kW, and source
at the receiving end receives 24.57 kW. Similarly, since QS is negative, source at the sending
end receives 21 kvar and source at the receiving end delivers 32.76 kvar. (b) The real power
loss is 3.43 kW. The reactive power loss in the line is 11.76 kvar.
Question 2
Repeat Question 1 assuming a lossless line