# Questions & Answers of System Stability Concepts

## Weightage of System Stability Concepts

Total 11 Questions have been asked from System Stability Concepts topic of Power Systems subject in previous GATE papers. Average marks 1.82.

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

Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator $G_1$ and $G_2$ are $Q_{G1}$ and $Q_{G2}$ respectively. The per unit values of $Q_{G1},$ and $Q_{G2},$ and line reactive power loss $(Q_{loss})$ respectively are

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 circuit 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 values of  $P_{max}$, in pu is ________ . (Give the answer up to three decimal places.)

The range of $K$ for which all the roots of the equation $s^3+3s^2+2s+K=0$ are in the left half of the complex s-plane is

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 aped and delivering 60 MW 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.

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 5º, 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 ________.

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?

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

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

Consider a synchronous generator connected to an infinite bus by two identical parallel transmission line. The transient reactance ‘x’ of the  generator is 0.1 pu and the mechanical power input to it is constant at 1.0 pu. Due to some previous disturbance, the rotor angle ($\delta$) is undergoing an undamped oscillation, with the maximum value of $\delta \left(t\right)$ equal to 130% .One of the parallel lines trip due to the relay maloperation at an instant when $\delta \left(t\right)$ = 130° 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