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