Question

1. A 3-phase, 20 kVA, 208 V, 4-pole Y-connected synchronous generator has a synchronous reactance of X_s = 1.5 W per phase. The resistance of the stator winding is negligible. The machine is connected to a 3-phase 208 V infinite bus. Neglect losses.

1. The field current and the mechanical input power are adjusted so that the synchronous machine delivers 10 kW at 0.8 lagging power factor. Determine the excitation voltage E_f and the power angle d.
2. The mechanical input power is kept constant but the field current is adjusted to make the power factor unity. Determine the percent change in the field current with respect to its value in part (a).

Answer 1

Ans)

Given ,

a)

The phase voltage is given as

The phase current is given as

negative sign in angle for lagging pf as current lags voltage

now  excitation voltage E_f is given as

the line voltage is

power angle

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b)

As the mechanical input power is kept constant ,the power P is also constant

for unity power factor

The phase current is given as

now  excitation voltage E_f is given as

The field voltage is proportional to field current hence

so percentage change in field voltage is same as field current using this