Question

A 2-phase, 3-wire a.c. system has a middle conductor of same cross-sectional area as the outer and supplies a load of 20 MW. The system is converted into 3-phase, 4-wire system by running a neutral wire. Calculate the new power which can be supplied if voltage across consumer terminal and percentage line losses remain the same. Assume balanced load.

Answer 1

The two systems are shown in Fig. Let R be the resistance per conductor.

P1 = 2V I1 cos φ; Cu loss, W1 = 2I12 R

Percentage Cu loss

= (W1/P1) × 100

= (2I2 R/2VI1 cos φ) × 100

= I1R × 100/V cos φ

P2 = 3VI2 cos φ

W2 = 3I2 2 R

% line loss = (W2/P2) × 100

= (3I22 R/3VI2 cos φ) × 100

= I2R × 100/V cos φ

Since percentage line losses are the same in both cases

∴ I1R × 100/V cos φ = I2R × 100/V cos φ

∴ I1 = I2

Now, P1 = 2VI1 cos φ = 20 MW ;

∴ VI1 cos φ = 10 MW

P2 = 3VI2 cos φ = 3VI1 cos φ = 3 × 10 = 30 MW