Power System Stability · Power System Analysis · GATE EE

Marks 1

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

GATE EE 2018

Shunt reactors are sometimes used in high voltage transmission systems to

GATE EE 2014 Set 2

The angle $$\delta $$ in the swing equation of a synchronous generator is the

GATE EE 2013

A round rotor generator with internal voltage $${E_1} = 2.0\,\,$$ p.u.and $$\,X = 1.1\,\,$$ p.u. is connected to a round rotor synchronous motor with internal voltage $$\,\,{E_2} = 1.3\,\,$$ p.u. and $$\,X = 1.2\,\,$$ p.u. The reactance of the line connecting the generator to the motor is $$0.5$$ p.u. when the generator supplies $$0.5$$ p.u. power, the rotor angle difference between the machines will be

GATE EE 2003

Steady state stability of a power system is the ability of the power system to

GATE EE 1999

A $$100$$ $$MVA$$, $$11$$ $$kV$$, $$3$$-phase, $$50$$ $$Hz$$, $$8$$-pole synchronous generator has an inertia constant H equal to $$4$$ $$MJ/MVA.$$ The stored energy in the rotor of the generator at synchronous speed will be $$H = {E \over G}$$

GATE EE 1997

During a disturbance on synchronous machine, the rotor swings from A to B before finally settling down to a steady state at a point C on the power angle curve. The speed of the machine during oscillation is synchronous at point(s)

GATE EE 1996

The transient stability of the power system can be effectively improved by

GATE EE 1993

Marks 2

The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the generator being $P_{max} \sin \delta$, where $\delta$ is the load angle and the mechanical power input is $0.5 P_{max}$. A fault occurs on line 2 such that the power output of the generator is less than $0.5 P_{max}$ during the fault. After the fault is cleared by opening line 2, the power output of the generator is $\left\{\frac{P_{max}}{\sqrt{2}} \right\} \sin \delta$. If the critical fault clearing angle is $\frac{\pi}{2}$ radians, the accelerating area on the power angle curve is ______ times $P_{max}$ (rounded off to 2 decimal places).

GATE EE 2024

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).

GATE EE 2022

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).

GATE EE 2022

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.

GATE EE 2017 Set 2

The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is $$\,1.5\,\,\sin \delta ,\,\,$$ where $$\delta $$ 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 $$\delta ,$$ as the rotor swings is $$1.221$$ radian. If the expression for electrical power with one transmission line circuit removed is $$\,{P_{\max }}\,\sin \delta ,\,\,$$ the valueof $${P_{\max }}\,,$$ in pu is _________.

GATE EE 2017 Set 1

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 $$\delta $$ is $${5^ \circ }$$, 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 $$\delta $$ in degrees, 0.02 second after the fault is _____________

GATE EE 2015 Set 1

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 t₁ 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?

GATE EE 2015 Set 2

The figure shows the single line diagram of a single machine infinite bus system.

The inertia constant of the synchronous generator $$𝐻 = 5$$ $$MW-s/MVA.$$ Frequency is $$50Hz.$$ Mechanical power is $$1$$ pu. The system is operating at the stable equilibrium point with rotor angle $$\delta $$ equal to $${30^ \circ }$$. 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 $$\,{P_{\max }}\,\,\sin \delta .\,\,\,$$. If the values of $$\delta $$ and $$d$$$$\delta $$$$/dt$$ at the instant of fault clearing are $${45^ \circ }$$ and $$3.762$$ radian/s respectively, then $$\,{P_{\max }}$$ (in pu) is _________.

GATE EE 2014 Set 3

A cylindrical 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 $$5$$ $$MW-s/MVA$$ 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

GATE EE 2012

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 $$\,\,27.5\,\, \times \,\,{10^3}\,\,kg\,\,{m^2}.\,\,$$ The inertia constant $$(H)$$ will be

GATE EE 2009

A lossless single machine infinite bus power system is shown below:

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

GATE EE 2008

Consider a synchronous generator connected to an infinite bus by two identical parallel transmission lines. The transient reactance $$x'$$ of the generator $$0.1$$ pu. Due to some previous disturbance, the rotor angle $$(d)$$ is undergoing an undamped oscillation, with the maximum value of $$\delta \left( t \right)$$ equal to $$\,{130^ \circ }\,.$$ One of the parallel lines trip due to relay mal-operation at an instant $$\,\,\,\,\,$$ when $$\,\delta \left( t \right)\,\, = {130^ \circ }\,\,$$ as shown in the figure. The maximum value of the per unit line reactance $$x,$$ such that the system does not lose synchronism subsequent to this tripping is

GATE EE 2007

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 $$5$$ MJ/MVA and it was delivering 1.0 pu power prior of the fault with rotor power angle of $${30^ \circ }\,\,$$. The system frequency is 50Hz.

The initial accelerating power (in pu) will be

GATE EE 2006

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 $$5$$ MJ/MVA and it was delivering $$1.0$$ pu power prior of the fault with rotor power angle of $${30^ \circ }\,\,$$. The system frequency is 50Hz.

If the initial accelerating power is $$X$$ pu, the initial acceleration in elect deg/sec², and the inertia constant in MJ-sec/elect deg respectively will be

GATE EE 2006

A generator with constant 1.0 p.u. terminal voltage supplies power through a step-up transformer of 0.12 p.u. reactance and a double-circuit line to an infinite bus bar as shown in the figure. The infinite bus voltage is maintained at 1.0 p.u. Neglecting the resistances and susceptances of the system, the steady state stability power limit of the system is 6.25 p.u. If one of the double-circuit is tripped, the resulting steady state stability power limit in p.u. will be

GATE EE 2005

A 50 Hz, 4-pole, 500 MVA, 22 kV turbo-generator is delivering rated megavolt-amperes at 0.8 power factor. Suddenly a fault occurs reducing is electric power output by 40%. Neglect losses and assume constant power input to the shaft. The accelerating torque in the generator in MNm at the time of fault will be

GATE EE 2004

A generator delivers power of 1.0 p.u. to an infinite bus through a purely reactive network. The maximum power that could be delivered by the generator is 2.0 p.u. A three-phase fault occurs at the terminals of the generator which reduces the generator output to zero. The fault is cleared after $${t_c}$$ seconds. The original network is then restored. The maximum swing of the rotor angle is found to be $${\delta _{\max }} = 110$$ electrical degree. Then the rotor angle in electrical degrees at $$t = {t_c}$$ is

GATE EE 2003

A transmission line has a total series reactance of 0.2 pu. Reactive power compensation is applied at the midpoint of the line and it is controlled such that the midpoint voltage of the transmission line is always maintained at 0.98 pu. If voltage at both ends of the line are maintained at 1.0 pu, then the steady state power transfer limit of the transmission line is

GATE EE 2002

A power station consists of two synchronous generators A and B of ratings 250 MVA and 500 MVA with inertia constant 1.6 p.u. and 1.0 p.u., respectively on their own base MVA ratings. The equivalent p.u. inertia constant for the system on 100 MVA common base is

GATE EE 1998

Marks 5

A synchronous generator is to be connected to an infinite bus through a transmission line of reactance X = 0.2 pu, as shown in figure the generator data is as follows:

X¹ = 0.1 pu, E¹ = 1.0 pu, H = 5 MJ/MVA, mechanical power P_m = 0.0 pu, $$\omega $$_B = 2 $$\pi \times $$50 rad/sec. All quantities are expressed on a common base.

The generator is initially running on open circuit with the frequency of the open circuit voltage slightly higher than that of the infinite bus. If at the instant of switch closure $$\delta = 0$$ and $$\omega = {{d\delta } \over {dt}} = {\omega _{init}},$$ compute the maximum value of $${\omega _{init}}$$ so that the generator pulls into synchronism.

$$\int {\left( {{{2H} \over {{\omega _B}}}} \right)\omega d\omega + {P_e}d\delta = 0} $$

GATE EE 2002

A synchronous generator is connected to an infinite bus through a lossless double circuit transmission line. The generator is delivering 1.0 per unit power at a load angle of $${30^0}$$ when a sudden fault reduces the peak power that can be transmitted to 0.5 per unit. After clearance of fault, the peak power that can be transmitted becomes 1.5 per unit. Find the critical clearing angle.

GATE EE 2001

A synchronous generator, having a reactance of 0.15 p.u., is connected to an infinite bus through two identical parallel transmission lines having reactance of 0.3 p.u. each. In steady state, the generator is delivering 1 p.u. Power to the infinite bus. For a three phase fault at the receiving end of one line, calculate the rotor angle at the end of first time step of 0.05 seconds. Assume the voltage behind transient reactance for the generator as 1.1 p.u. and infinite bus voltage as 1.0 p.u. Also indicate how the accelerating powers will be evaluated for the next time step if the breaker clears the fault.

(i) at the end of an interval
(ii) at the middle of an interval.

GATE EE 2000

An alternator is connected to an infinite bus as shown in figure. It delivers 1.0 p.u. current at 0.8 p.f lagging at V = 1.0 p.u.. The reactance X_d of the alternator is 1.2 p.u. Determine the active power output and the steady state power limit. Keeping the active power fixed, if the excitation is reduced, find the critical excitation corresponding to operation at stability limit.

GATE EE 1998

A synchronous motor is receiving 50% of the power it is cable to receiving from an infinite bus. If the load on the motor is suddenly reduced to 80% of the previous value, swing of the motor around is new equilibrium position.

GATE EE 1997

In a system, there are two generators operating in parallel. One generator, of rating 250 MVA, has an inertia-constant of 6 MJ/MVA while the other generator of 150 MVA has an inertia-constant of 4 MJ/MVA. The inertia-constant for the combined system on 100 MVA common base is ________MJ/MVA.

GATE EE 1994