Steady State Stability & Transient Stability

Q. Steady state stability of power system is the ability of the power system to

1. maintain voltage at the rated voltage level
2. maintain frequeny exactly at 50 Hz
3. 
   maintain a spinning reserve mrgin at all times
4. maintain synchronism

Q. 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

1. 31.4 X, 18
2. 1800 X, 0.056
3. X/1800, 0.056
4. X/31.4, 18

Q. S1 : To increase the steady state stability limit, we use parallel transmission line.
S2: Using parallel transmission lines increases the value of reactance.

1. Both S1 and S2 are individually true and S2 is the correct explanation of S1.
2. Both S1 and S2 are individually true but S2 is not the correct explanation of S1.
3. S1 is true but S2 is false.
4. S1 is false but S2 is true.

Q. An 800 kV transmission line has a maximum power transfer capacity of P. If it is operated at 400 kV with the series reactance unchanged, then new maximum power transfer capacity is approximately

1. P
2. 2P
3. P/2
4. P/4

Q. The load carrying capability of long AC transmission line is

1. always limited by the conductor size.
2. limited by stability considerations.
3. reduced at low ambient temperature.
4. decreased by the use of bundled conductors of single conductors.

Q. A transmission line of inductance 0.1 H and resistance 5$\Omega$ is suddenly short-circuit at the far end as shown in figure.




Select the correct statement

1. The complementary solution of short circuit current is given by
   $3.1435\sin (100\pi t-{65.96}^{\circ })A$
2. The particular solution of short circuit current is given by
   $2.871e^{-50t}A$
3. Expression of short circuit current is
   $3.1435sin(100\pi t-{65.96}^{\circ })+2.871e^{-50t}A.$
4. If switch is closed when $v$ is maximum then value of short circuit current at that moment is 2.871A

Q. Consider a lossy transmission line with $V_1$ and $V_2$ as the sending and receiving end voltages, respectively. Z and X are the series impedance and reactance of the line, respectively. The steady-state stability limit for the transmission line will be

1. greater than $\left|\frac{V_1{V}_2}{X}\right|$
2. less than $\left|\frac{V_1{V}_2}{X}\right|$
3. equal to $\left|\frac{V_1{V}_2}{X}\right|$
4. equal to $\left|\frac{V_1{V}_2}{X}\right|$

Q. The synchronous generator shown in the figure is supplying active power to an infinite bus via two short lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude E are constant. If one line is tripped at time
$t_1$ by opening the circuit breakers at the two ends (although there is no fault), then it is seen that the generator undergoes a stable transient. Which one of the following waveforms of the rotor angle $\delta$ shows the transient correctly?

1. 
2. 
3. 
4. 

Q. The terminal voltage of the generator is held at 1.20 p.u. and the voltage of the infinite bus is 1.0 p.u. The value of steady state power limit of a system consisting of a generator equivalent reactance 0.5 p.u. connected to an infinite bus through a series reactance of 1.0 p.u. is

1. 2.512 p.u.
2. 0.591 p.u
3. 1.151 p.u.
4. 1.615 p.u.