Question

A 3-phase, 50 Hz, synchronous generator has rating 200 MVA, The Kinetic energy of the machine at synchronous speed is 800 MJ. The machine is running steadily at synchronous speed and delivering 50 MW power at power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 8 cycles, the value of power angle after 4 cycles is ___________electrical degrees.

• A. 11.81

Answer 1

The correct option is A 11.81
$Given,P_e=50MW$

$K.E.=800MJ$

$f=50Hz;$

${\delta }_0={10}^{\circ }$

$Timefor8cycles=\frac{8}{50}=0.16sec$

$Timefor4cycle0.08sec$

$P_a=50MW$

$M=\frac{K.E.}{180f}=\frac{GH}{180\times f}$

$M=\frac{800}{180\times 50}=0.088$

We know that, $M\frac{d^2\delta }{d{t}^2}=P_a$

$\frac{d^2\delta }{d{t}^2}=\frac{P_a}{M}$

Integrating twice we have,

$\delta =\frac{P_a}{M}\left[\frac{t^2}{2}\right]+{\delta }_0=\frac{50}{0.088}\left[\frac{{0.08}^2}{2}\right]+{10}^{\circ }$

$\text{New value of power angle}={1.81}^{\circ }+{10}^{\circ }={11.81}^{\circ }$