Question

Find the following for a single-circuit transmission line delivering a load of 50 MVA at 110 kV and p.f. 0.8 lagging :

(i) sending-end voltage, (ii) sending-end current, (iii) sending-end power, (iv) efficiency of transmission. (Given A = D = 0.98 ∠3 , B = 110 ∠75 ohm, C = 0.0005 ∠80 ohm)

Answer 1

Receiving-end voltage, VR = 110/ √3 = 63.5 kV

Taking this voltage as reference voltage, we have

DIR = 0.98∠3 × 262.4 ∠36.86 = 257.75 ∠39.86 = 197.4 + j 164.8

(ii) IS = CVR + DIR = 203 + j 196 = 282 ∠44A

(iii) Sending-end power = 3VS IS cos φS = 3 × 59.565 × 282 × cos ∠44.30 − 30.3 = 48.96 MW

Receiving end power = 50 × 0.8 = 40 MW

(iv) Transmission η = 40 × 100/48.96 = 81.7%