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Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE) PDF Download

Q1: A 20 MVA, 11.2 kV, 4-pole, 50 Hz alternator has an inertia constant of 15 MJ/MVA. If the input and output powers of the alternator are 15 MW and 10 MW, respectively, the angular acceleration in mechanical degree/s2 is __________. (round off to nearest integer)      (2022)
(a) 25
(b) 50
(c) 75
(d) 100
Ans:
(c)
Sol: We have, swing equation
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Put the values,
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Q2: Two generating units rated for 250 MW and 400 MW have governor speed regulations of 6% and 6.4%, respectively, from no load to full load. Both the generating units are operating in parallel to share a load of 500 MW. Assuming free governor action, the load shared in MW, by the 250 MW generating unit is _________. (round off to nearest integer)       (2022)
(a) 100
(b) 150
(c) 200
(d) 250
Ans: 
(c)
Sol: Let no-load frequency is 50 Hz.
Draw the curve :
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)From the curve,
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)From eq. (1) & (2),
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Q3: In the figure shown, self-impedances of the two transmission lines are 1.5j p.u each, and Zm = 0.5jp.u is the mutual impedance. Bus voltages shown in the figure are in p.u. Given that δ > 0, the maximum steady-state real power that can be transferred in p.u from Bus-1 to Bus-2 is      (2021)
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)(a) |E| |V|
(b) (|E| |V|)/2
(c) 2 |E| |V|
(d) (3|E| |V|)/2
Ans:
(a)
Sol: Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Q4: In the single machine infinite bus system shown below, the generator is delivering the real power of 0.8pu at 0.8 power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is _________       (2019)
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)(a) 12.8
(b) 28.4
(c) 20.5
(d) 32.6
Ans: 
(c)
Sol: Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Q5: Consider a lossy transmission line with V1 and V2 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      (2018)
(a) greter than Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)

(b) less than Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
(c) equal to Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
(d) equal to Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Ans: (b)
Sol: With only x:
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)With Lossy Tr, Line
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Q6: 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.      (SET-2  (2017))
(a) 1.27
(b) 2.7
(c) 12.7
(d) 127
Ans:
(c)
Sol: Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Load is removed,
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)So, new value of power angle
= 10° + 2.7° = 12.7°

Q7: The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is 1.5 sinδ, where δ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to 1 pu. If one of the transmission line circuits is removed, the maximum value of δ as the rotor swings, is 1.221 radian. If the expression for electrical power with one transmission line circuit removed is Pmaxsinδ, the value of Pmax, in pu is _________.     (SET-1  (2017))
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)(a) 0.729
(b) 1.22
(c) 2.6
(d) 4.8
Ans:
(b)
Sol: Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Using equal area criteria:
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)By solving above integration,
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Given data:
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Substitute above values in above equation,
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Q8: 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 tby 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 δδ shows the transient correctly?       (SET-2 (2015))
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)(a) Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)(b) Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)(c) Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)(d) Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Ans:
(a)
Sol: Initial value of δ = δ0 at t = t1 with both lines are in service of one of the line circuit breakes opened the δ is increased for same time and stabilizes to new value of δ.

Q9: A 50 Hz generating unit has H-constant of 2 MJ/MVA. The machine is initially operating in steady state at synchronous speed, and producing 1 pu of real power. The initial value of the rotor angle  δ is 5°, when a bolted three phase to ground short circuit fault occurs at the terminal of the generator. Assuming the input mechanical power to remain at 1 pu, the value of δ in degrees, 0.02 second after the fault is _________.        (SET-1 (2015))
(a) 0.5
(b) 2.8
(c) 4.2
(d) 5.9
Ans:
(d)
Sol: Let 3 − ϕ fault occurs at t = 0
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Now, swing equation for t ≥ 0+
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Now in problem,
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Q10: The figure shows the single line diagram of a single machine infinite bus system.
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)The inertia constant of the synchronous generator H = 5 MW-s/MVA. Frequency is 50 Hz. Mechanical power is 1 pu. The system is operating at the stable equilibrium point with rotor angle δ equal to 30°. A three phase short circuit fault occurs at a certain location on one of the circuits of the double circuit transmission line. During fault, electrical power in pu is Pmax sin δ . If the values of δ and dδ/dt at the instant of fault clearing are 45° and 3.762 radian/s respectively, then Pmax (in pu) is ______.       (SET-3 (2014))
(a) 0.11
(b) 0.23
(c) 0.48
(d) 0.64
Ans:
(b)
Sol: Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Multiplying with ωr in both side
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)In problem,
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Q11: There are two generators in a power system. No-load frequencies of the generators are 51.5 Hz and 51 Hz, respectively, and both are having droop constant of 1Hz/MW. Total load in the system is 2.5 MW. Assuming that the generators are operating under their respective droop characteristics, the frequency of the power system in Hz in the steady state is ______.       (SET-2 (2014))
(a) 25
(b) 50
(c) 75
(d) 100
Ans: 
(b)
Sol: Let no-load frequency of generator-1 be 51.5 Hz and no-load frequency of generator-2 be 51 Hz.
Given total load = 2.5 Mwand drop of both machines = 1 Hz/MW
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Let machine-1 shares a load of P1 MW them machine-2 will share a load of (2.5 − P1) MW
Le the steady state frequency of the system be f.
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Q12: A synchronous generator is connected to an infinite bus with excitation voltage E= 1.3 pu. The generator has a synchronous reactance of 1.1 pu and is delivering real power (P) of 0.6 pu to the bus. Assume the infinite bus voltage to be 1.0 pu. Neglect stator resistance. The reactive power (Q) in pu supplied by the generator to the bus under this condition is _____.       (SET-2 (2014))
(a) 0.8
(b) 0.11
(c) 0.45
(d) 1.82
Ans:
(b)
Sol: Given, Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Neglecting stator resistance i.e. θs = 90°
Output power delivered,
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Reactive power is given by,
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Q13: A cylinder rotor generator delivers 0.5 pu power in the steady-state to an infinite bus through a transmission line of reactance 0.5 pu. The generator no-load voltage is 1.5 pu and the infinite bus voltage is 1 pu. The inertia constant of the generator is 5MW-s/MVA and the generator reactance is 1 pu. The critical clearing angle, in degrees, for a three-phase dead short circuit fault at the generator terminal is       (2012)
(a) 53.5
(b) 60.2
(c) 70.8
(d) 79.6
Ans:
(d)
Sol: Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Critical clearing angle
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Q14: A 500 MW, 21 kV, 50 Hz, 3-phase, 2-pole synchronous generator having a rated p.f = 0.9, has a moment of inertia of 27.5 × 103kg − m2. The inertia constant (H) will be      (2009)
(a) 2.44s
(b) 2.71s
(c) 4.88s
(d) 5.42s
Ans:
(a)
Sol: J = moment of inertia = 27.5 × 103kg − m2
Synchronous speed
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Kinetic energy of the rotor
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)K.E. = 1375 MJ
G = Machine rating Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Inertia constant Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)

Q15: A loss less single machine infinite bus power system is shown below :
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)The synchronous generator transfers 1.0 per unit of power to the infinite bus. The critical clearing time of circuit breaker is 0.28 s. If another identical synchronous generator is connected in parallel to the existing generator and each generator is scheduled to supply 0.5 per unit of power, then the critical clearing time of the circuit breaker will       (2008)
(a) reduce to 0.14 s
(b) reduce but will be more than 0.14 s
(c) remain constant at 0.28 s
(d) increase beyond 0.28 s
Ans:
(d)
Sol: Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)For such faults,
δcr is given by
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)CASE-1:
When only once generator is connected
Mechanical input to the generator Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE) = Electrical power delivered by the generator Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE) Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)CASE-2:
When two generator connected in parallel
Electrical power delivered by each generator
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)
Mechanical inout to each generator
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)Assuming δ0 in each case same
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)So, δcr will also be same in both cases, (from equation (i)),
Previous Year Questions- Power System Stability - 1 | Power Systems - Electrical Engineering (EE)

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FAQs on Previous Year Questions- Power System Stability - 1 - Power Systems - Electrical Engineering (EE)

1. What is power system stability and why is it important in electrical engineering?
Ans. Power system stability refers to the ability of an electrical power system to maintain a state of equilibrium during normal operating conditions and also when subjected to disturbances. It is important because it ensures the continuous and reliable operation of the power system, preventing blackouts and maintaining system integrity.
2. What are the different types of power system stability?
Ans. The different types of power system stability include: 1. <b>Transient Stability</b> - the ability of the system to maintain synchronism following a transient disturbance such as a fault. 2. <b>Steady-State Stability</b> - the ability to maintain synchronism under steady-state conditions. 3. <b>Dynamic Stability</b> - the ability to maintain stability over a range of operating conditions and disturbances over time.
3. What factors affect power system stability?
Ans. Factors that affect power system stability include system configuration, load characteristics, generator characteristics, the presence of synchronous and asynchronous machines, system damping, fault conditions, and the control strategies employed in the power system.
4. How can power system stability be improved?
Ans. Power system stability can be improved through various methods such as: 1. <b>Increased Damping</b> - using power system stabilizers or FACTS devices. 2. <b>Proper Control Strategies</b> - implementing automatic generation control and load frequency control. 3. <b>Network Design</b> - optimizing the transmission network to reduce impedance and enhance interconnections.
5. What is the role of dynamic simulations in analyzing power system stability?
Ans. Dynamic simulations play a crucial role in analyzing power system stability by modeling the system's response to disturbances over time. They help engineers to visualize and understand the behavior of the power system under various scenarios, allowing for the design of effective control strategies and improvement measures.
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