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 this 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,

$Theveninimpedance,Z_{th}=(0.2+0.1)||(0.2+X)$
$=\frac{\left(0.3\right)(0.2+X)}{0.5+X}$

$Also,perunitfaultcurrent=\frac{1}{Z_{th}}=6pu$

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

$0.5+X=\left(1.8\right)(0.2+X)$

$0.8X=0.5-0.36orX=0.175pu$

Now using X = 0.175 pu, finding fault level at bus 3 after interconnection
$New,Z_{thpu}=\frac{\left(0.5\right)\left(0.175\right)pu}{0.675}=0.1296pu$
$I_f^{\prime }=\frac{1}{Z_{thpu}}=7.71pu$