Question

A 150 km, 3-φ, 110-V, 50-Hz transmission line transmits a load of 40,000 kW at 0.8 p.f. lag at receiving end

resistance/km/phase = 0.15 Ω, reactance/km/phase = 0.6 Ω ; susceptance/km/phase = 10⁻⁵ S 

(a) determine the A, B, C and D constants of the line 

(b) find regulation of the line.

Answer 1

We will use the nominal-π method to solve the problem. For a length of 150 km : 

R = 0.15 × 150 = 22.5 Ω ; X = 0.6 × 150 = 90 Ω ; Y = 150 × 10⁻⁵ S = 15 × 10⁻⁴ S 

Z = (R + j X) = (22.5 + j 90) = 92.8 ∠75º ohm ; Y = 15 × 10⁻⁴ ∠90º S

(b) Now, the regulation at the receiving-end is defined as the change in voltage when full-load is thrown off, the sending-end voltage being held constant.

Now, when load is thrown off, I_R = 0. Hence, putting this value in V_S = AV_R + BI_R, we get