Question

A power system has a circuit breaker connecting a large system, (initially open) to other system between bus 2 and bus 3. The system B three-phase fault level at bus 3 under the condition is unknown. After closing circuit breaker, the 3$-\varphi$ fault level at bus 1 was found to be 6 pu. The new 3$-\varphi$ fault level at system bus 3 after interconnection will be _______pu.(Assume prefault voltages to be 1 pu at all buses).

• A. 7.71

Answer 1

The correct option is A 7.71
Drawing single line diagram, assuming system B reactance be X,



If fault occurs at bus 1 after reactance,



Thevenin impedance, $Z_{th}=(0.2+0.1)||(0.2+X)$

$=\frac{\left(0.3\right)(0.2+X)}{0.5+X}$

Also, per unit fault current $=\frac{1}{Z_{th}}=6$ pu

$\therefore$ $\frac{1}{6}=\frac{\left(0.3\right)(0.2+X)}{0.5+X}$

0.5 + X = (1.8) (0.2 + X)
0.8 X = 0.5 - 0.36 or X = 0.175 pu

Now using X = 0.175 pu, finding fault level at bus 3 after interconnection

New, $Z_{thpu}=\frac{\left(0.5\right)\left(0.175\right)}{0.675}=0.1296pu$

$I_f^{\prime }=\frac{1}{Z_{thpu}}=7.71$ pu