Question

A 50-Hz, 3-phase, 100-km long line delivers a load of 40 MVA at 110 kV and 0.7 p.f. lag. The line constants (line to neutral) are : resistance of 11 ohms, inductive reactance of 38 ohms and capacitive susceptance of 3 × 10⁻⁴ siemens. Find the sending-end voltage, current, power factor and efficiency of power transmission.

(b) draw the vector diagram. 

(c) If the sending-end voltage is held constant and load is removed, calculate the receiving-end voltage and current.

Answer 1

(a) Nominal π-method will be used to solve this problem. Capacitive susceptance (or admittance) at each end = Y /2 = 3 × 10⁻⁴ /2 = 1.5 × 10⁻⁴ siemens as shown in Fig. 

As seen from Fig.

Line value of sending-end voltage

Angle between V_S and I_S = 41.6º + 3.2º = 44.8º;

cos φ_S = cos 44.8º = 0.71 (lag)

Power input = √3 × 122.2 × 10³ × 195.7 × 0.7 = 29.41 MW 

Power output = 40 × 0.7 = 28 MW

∴ power transmission η = 28/29.41 = 0.952 or 95.2% 

(b) vector diagram is similar to that shown in Fig.(b).

 

(c) As seen from Fig.under no-load condition, current in the conductor is