Question

A 50 Hz alternator is rated 500 MVA, 20 kV, with X${}_d$ = 1.0 per unit and X${}_d^{\prime \prime }$ = 0.2 per unit. It supplies a purely resistive load of 400 MW at 20 kV. The load is connected directly across the generator terminals when a symmetrical fault occurs at the load terminals. The initial rms current in the generator in per unit is

• A. 7.22
• B. 5.05
• C. 3.22
• D. 2.25

Answer 1

The correct option is B 5.05


P${}_{3-\varphi (p.u.)}$ = V${}_{p.u.}$ I${}_{p.u.}$ Cos$\Theta$

P${}_{p.u.}$ = $\frac{400}{500}$ = 0.8 p.u.

($\because$ Base MVA = 500 MVA)

(P${}_{actual}=400MW$)

Since, V${}_{(}p.u.)$ = 1$\angle 0^0$ p.u.

$\therefore$ I${}_{p.u.}$ = 0.8

E${}_g^{\prime \prime }$ = 1$\angle 0^0$ + j0.2(0.8 $\angle 0^0$)

= 1.01 $\angle {9.09}^0$ p.u.

I${}_f^{\prime \prime }$ = $\frac{1.01}{0.2}$ = 5.05 p.u.