Question

(a) How do the leakage fluxes effect the operation of a transformer? How are they minimized? (6)

(b) A 440 V load of 400 kw at 0.8 (lagging) power factor is jointly supplied by two alternators A and B. The KW load on A is 150 KW and the KVAr load on B is 150 kVA (lagging). Determine the kW load on B, the KWAr load on A, the power factor of operation on each machine and the current loading of each machine. (10)

Answer 1

Part (a)

Effect of leakage fluxes on the operation of a transformer, and how they are minimised:

Leakage flux is the flux that links only one winding (primary or secondary) and not the other. It does not contribute to the transfer of energy but produces a leakage reactance in each winding.
Effects: the leakage reactance causes a voltage drop in the transformer, so the secondary voltage falls with load (voltage regulation). It also limits the short-circuit current (which is beneficial for protection) and causes a phase shift between the primary and secondary voltages. Excessive leakage flux increases the reactance and worsens the voltage regulation.
Minimisation: leakage flux is reduced by interleaving the primary and secondary windings (placing them close together, e.g. concentric or sandwich windings), by using a low-reluctance magnetic path, and by proper winding arrangement. The leakage reactance is designed to give the required short-circuit current limiting while keeping the voltage regulation acceptable.

Part (b)

440 V load of 400 kW at 0.8 p.f. lagging supplied by two alternators A and B. kW on A = 150 kW, kVAr on B = 150 kVAr (lagging).

Total kW = 400 kW. Total kVA = 400/0.8 = 500 kVA. Total kVAr = 500 x 0.6 = 300 kVAr (lagging).
kW on B = 400 - 150 = 250 kW.
kVAr on A = 300 - 150 = 150 kVAr (lagging).
Machine A: kVA = sqrt(150^2 + 150^2) = 212.1 kVA. p.f. = 150/212.1 = 0.707 lagging.
Machine B: kVA = sqrt(250^2 + 150^2) = 291.5 kVA. p.f. = 250/291.5 = 0.858 lagging.
Current: I = S/(root 3 x 440). I_A = 212100/762.1 = 278.3 A. I_B = 291500/762.1 = 382.5 A.

So A supplies 150 kW at 0.707 p.f. lagging (278 A); B supplies 250 kW at 0.858 p.f. lagging (382 A).

✓ Verified Model Answer (Text Solution)

Effect of leakage fluxes on the operation of a transformer, and how they are minimised:

440 V load of 400 kW at 0.8 p.f. lagging supplied by two alternators A and B. kW on A = 150 kW, kVAr on B = 150 kVAr (lagging).