Equal Area Criteria: Effect of Clearing time on Stability

Q. A synchronous generator of reactance 1.20 p.u. is connected to an infinite bus bar through transformers and a line of total reactance of 0.6 p.u. The generator no load voltage is 1.20 p.u. and its inertia constant is H = 4 MWs/MVA. The resistance and machine damping may be assumed negligible. The system frequency is 50 Hz. If the generator is loaded to 50% of the maximum power limit, then the frequency of natural oscillations is

1. 4.76 Hz
2. 0.764 Hz
3. 3.52 Hz
4. 0.467 Hz

Q. A 50 Hz generator is delivering 60% of power that it is capable of delivering through a transmission line to an infinite bus. A fault occurs that increases the reactance between the generator and the infinite bus to 400% of the value before the fault. When fault is isolated, the maximum power that can be delivered is 75% of the original maximum value. For this condition critical clearing angle (in degres) is

1. ${67.33}^o$
2. ${54.17}^o$
3. ${36.86}^o$
4. ${51.32}^o$

Q. A 50 Hz generator is delivering rated power of 1.0 p.u. to an infinite bus through a lossless network. A three phase fault under this condition reduces $P_{\text{max}}$ to 0 per unit. If the fault is cleared in 0.05 sec, then the rotor angle at this instant is
(Assume $P_{\text{max}}$ before fault is 2.0 p.u. and 1.5 p.u. after fault clearing and H= 7.5 MJ/MVA)

1. 30 electrical degrees
2. 31.5 electrical degrees
3. 34.2 electrical degrees
4. 32.6 electrical degrees

Q. A 3-phase , 2-pole, 50 Hz, synchronous generator has a rating of 250 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running steadily at synchronous speed and delivering 60 MW power at a power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 10 cycles, the value of the power angle after 5 cycles is electrical degrees is.

1. 12.7

Q. 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]

1. ${60.24}^{\circ }$
2. ${45.40}^{\circ }$
3. ${81.72}^{\circ }$
4. ${75.80}^{\circ }$

Q. A motor is receiving 25% of the power that it is capable of receiving from an infinite bus, if the load on the motor is doubled, calculate the maximum value of $\delta$ during the swinging of the rotor around its new equilibrium position.

1. ${45.4}^{\circ }$
2. ${60}^{\circ }$
3. ${80}^{\circ }$
4. ${30}^{\circ }$

Q. A 50 Hz, four pole turbo generator rated 100 MVA, 11 kV has an inertia constant of 8.0 MJ/MVA. Mechanical input is suddenly raised to 80 MW for an electrical load of 50 MW. If the acceleration is maintained for 10 cycles, the rotor speed at the end of this period is

1. 1404.526 rpm
2. 1608.635 rpm
3. 1515.625 rpm
4. 1505.625 rpm

Q. A $3-\varphi$, 50 Hz, Y-connected, 100 MVA, 50 Hz alternator has inertia constant H = 5 MJ/MVA. Initially it delivers 60 MW at equilibrium. If the prime mover input is suddenly increased to 70 MW, then the load angle after 6 cycles is______ electrical degrees.

1. ${10.23}^{\circ }$
   
2. ${31.30}^{\circ }$
3. ${20.46}^{\circ }$
4. ${15.46}^{\circ }$

Q. A 60 Hz generator, connected directly to an Infinite bus operating at a voltage of $1\angle 0^{\circ }p.u.,$ has a synchronous reactance of 1.35 p.u. The generator no load voltage is 1.1 pu. and its inertia constant H is 4 MJ/MVA: The generator is suddenly loaded to 60 percent of its maximum power limit. The frequency of the resulting natural oscillations of the generator rotor is

1. 1.246 Hz
2. 0.882 Hz
3. 0.921 Hz
4. 1.16 Hz

Q. A 50 Hz, 4-pole turbo generator rated 100 MVA, 11 kV has an inertia constant of 10 MJ/MVA. If the mechanical input is suddenly raised to 90 MW for an electrical load of 60 MW. Neglect mechanical and electrical losses. Then the rotor acceleration is ______electrical degrees /sec${}^2$.

1. 270

Q.

An A.C source of voltage $V=220\sin (100\pi t)volts$ is connected with $R=50\Omega$. The time interval in which the current goes from its peak value to half of the peak value is

1. $\begin{array}{l}\frac{1}{400}\sec \end{array}$

2. $\begin{array}{l}\frac{1}{50}\sec \end{array}$

3. $\begin{array}{l}\frac{1}{300}\sec \end{array}$

4. $\begin{array}{l}\frac{1}{200}\sec \end{array}$

Q. A $3-\varphi$, 2 pole, 50 Hz, synchronous generator has rating of 200 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 840 MJ. The machine is operating at synchronous speed and delivering 50 MW power at a power angle of 10° electrical degree. If load is suddenly removed, assuming acceleration is constant for 10 cycles, the value of power angle after 5 cycles will be (in electrical degree)

1. 11.725°
2. 10.50°
3. 12.679°
4. 14.72°

Q. A $3-\varphi$, 2 pole, 50 Hz, synchronous generator has rating of 200 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 840 MJ. The machine is operating at synchronous speed and delivering 50 MW power at a power angle of 10° electrical degree. If load is suddenly removed, assuming acceleration is constant for 10 cycles, the value of power angle after 5 cycles will be (in electrical degree)

1. 11.725°
2. 10.50°
3. 12.679°
4. 14.72°