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 ∠3º , B = 110 ∠75º ohm, C = 0.0005 ∠80º ohm)

Answer 1

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

Taking this voltage as reference voltage, we have

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

(ii) I_S = CV_R + DI_R = 203 + j 196 = 282 ∠44ºA

(iii) Sending-end power = 3V_S I_S cos φ_S = 3 × 59.565 × 282 × cos ∠44.30º − 30.3º = 48.96 MW 

Receiving end power = 50 × 0.8 = 40 MW

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