Question

A 50 Hz, 3-phase, 33 kV synchronous generator is connected to a power system. The system inductance and capacitance per phase are 8 mH and 0.5 mF respectively. The value of restriking voltage at time t = 1.57 ms is

• A. 6.72 kV
• B. 7.88 kV
• C. 26.94 kV
• D. 20.66 kV

Answer 1

The correct option is B 7.88 kV

$V_R=V_m(1-cos\omega t)$

$\omega =\frac{1}{\sqrt{LC}}$

$V_m=$ per phase peak voltage

$\omega =\frac{1}{\sqrt{0.5\times {10}^{-3}\times 8\times {10}^{-3}}}=500rad/sec$

$V_m=\left(\frac{33}{\sqrt{3}}\right)\times \sqrt{2}kV=26.94kV$

at $t=1.57msec,$
$V_R=26.94(1-cos(500\times 1.57\times {10}^{-3}\left)\right)$

$V_R=7.88kV$ (Keep the calculator in radian mode)