Question

In the system shown, the generator is delivering 1 p.u. power. The voltage behind transient reactance is 1.05 p.u. and infinite bus voltage is 1 p.u. If the system is subjected to a $3-\varphi$ fault on point P, the critical clearing angle is______electrical degrees.[H=5 MJ/MVA.f = 50 Hz]

• A. ${60.24}^{\circ }$
• B. ${45.40}^{\circ }$
• C. ${81.72}^{\circ }$
• D. ${75.80}^{\circ }$

Answer 1

The correct option is C ${81.72}^{\circ }$

System reactance. X = j$(0.2+0.1+\frac{0.4}{2})=j0.5p.u.$

$P_s=\frac{V_s{V}_R}{X}sin\delta =\frac{1.05\times 1.0}{0.5}sin\delta =2.1sin\delta$

$P_s=1p.u$
$\therefore \delta =si{n}^{-1}\left(\frac{1}{2.1}\right)={28.44}^{\circ }=0.496radian\left(elec\right)$

${\delta }_c=co{s}^{-1}\left[\right(\pi -2{\delta }_0)sin{\delta }_0-cos{\delta }_0]$
$=co{s}^{-1}\left[\right(\pi -2\times 0.496)sin{28.44}^{\circ }-cos{28.44}^{\circ }]$
$={81.72}^{\circ }$ (electrical)