Question

Statement:
A generator feeds power to an infinite bus through a double circuit transmission line. A 3-phase fault occurs at the middle point of one of the lines. The infinite bus voltage is 1 pu, the transient internal voltage of the generator is 1.1 pu and the equivalent transfer admittance during fault is 0.8 pu. The 100 MVA generator has an inertia constant of 5MJ/MVA and it was delivering 1.0 pu power prior of the fault with rotor power angle of ${30}^{\circ }$. The system frequency is 50 Hz.

If the initial accelerating power is X pu, the initial acceleration in elect deg/$se{c}^2$, and the inertia constant in MJ-sec/elect deg respectively will be

• A. 31.4 X, 18
• B. 1800 X, 0.056
• C. X/1800, 0.056
• D. X/31.4, 18

Answer 1

The correct option is B 1800 X, 0.056

Inertia constant (in MJ-s/elec deg)
$=M=\frac{GH}{180f}$

where,
G= Machine rating =100 MVA
H= Inertia constant in MJ/MVA =5 MJ/MVA

$M=\frac{GH}{180f}=\frac{5\times 100}{180\times 50}$

=0.056 MJ-s/elec deg

$M_{(inp.u.)}=\frac{H}{180f}=\frac{5}{180\times 50}$

$\alpha$=Acceleration in elect deg/sec${}^2$

$M\alpha =P_a$

$P_a=$ Accelerating power =X

$\alpha \frac{P_a}{M}=\frac{X}{(5/180\times 50)}$

$=1800Xelecdeg/se{c}^2$