Question

An overhead, single-phase transmission line delivers 1100 kW at 33 kV at 0.8 p.f. lagging. The total resistance of the line is 10 Ω and total inductive reactance is 15 Ω. Determine (i) sending-end voltage (ii) sending-end p.f. and (iii) transmission efficiency

Answer 1

Full-load line current is I = 1100/33 × 0.8 = 41.7 A

Line loss = I² R = 41.7² × 10 = 17,390 W = 17.39 kW

(iii) Transmission efficiency

(i) Line voltage drop = IZ = 41.7(0.8 − j 0.6) (10 + j 15) = 709 + j 250 Sending-end voltage is

E_S = E_R + I_Z = (33,000 + j 0) + (709 + j 250)

= 33,709 + j 250 = 33,710 ∠25°

Hence, sending-end voltage is 33.71 kV

(ii) As seen from Fig. 41.22, α= 0°25′

Sending-end p.f. angle is

θ + α = 36°52′ + 0°25′ = 37°17′

∴ p.f. = cos 37°17′ = 0.795 (lag).

Note. As seen from Fig, approximate line drop is

= I(R cos φ_R + X sin φ_R) = 41.7 (10 × 0.8 + 15 × 0.6) = 709 V

∴ E_S = 33,000 + 709 = 33,709 V —as above