Electrical Engineering GATE 2021 Questions with Answer

Ques 53 Power Systems

A 3-Bus network is shown. Consider generators as ideal voltage sources. If rows 1, 2 and 3 of the Y_Bus matrix correspond to Bus 1, 2 and 3, respectively, then Y_Bus of the network is

Ques 54 Power Systems

Suppose I_A, I_B and I_C are a set of unbalanced current phasors in a three-phase system. The phase-B zero-sequence current I_B0 = 0.1∠0° p.u. If phase-A current I_A = 1.1∠0° p.u and phase-C current I_C = (1∠120° + 0.1) p.u., then I_B in p.u. is

Ques 55 Power Systems

Consider a power system consisting of N number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is N_L. The balanced Newton-Raphson method is used to carry out load flow study in polar form. H, S, M, and R are sub-matrices of the Jacobian matrix J as shown below:

Ques 56 Power Systems

Two generators have cost functions F₁ and F₂. Their incremental-cost characteristics are

Ques 57 Power Systems

Two single-core power cables have total conductor resistances of 0.7 Ω and 0.5 Ω, respectively, and their insulation resistances (between core and sheath) are 600 MΩ and 900 MΩ, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is _______ ×10⁶.

Ques 58 Power Systems

An alternator with internal voltage of 1<δ₁ p.u and synchronous reactance of 0.4 p.u is connected by a transmission line of reactance 0.1 p.u to a synchronous motor having synchronous reactance 0.35 p.u and internal voltage of 0.85<δ₂ p.u. If the real power supplied by the alternator is 0.866 p.u, then (δ₁ - δ₂) is _______ degrees. (Round off to 2 decimal places.)
(Machines are of non-salient type. Neglect resistances.)

Ques 59 Power Systems

In the figure shown, self-impedances of the two transmission lines are 1.5j p.u each, and Z_m = 0.5j p.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

Ques 60 Signals and Systems

Consider a continuous-time signal x(t) defined by x(t) = 0 for t > 1, and x(t) = 1 - |t| for |t| ≤ 1. Let the Fourier transform of x(t) be defined as X(ω) = ∫_-∞^∞ x(t) e^-jωt dt. The maximum magnitude of X(ω) is _______.

Ques 61 Signals and Systems

If the input x(t) and output y(t) of a system are related as y(t)=max(0,x(t)), then the system is

Ques 62 Signals and Systems

Two discrete-time linear time-invariant systems with impulse responses h₁[n]=δ[n-1]+δ[n+1] and h₂[n]=δ[n]+δ[n-1] are connected in cascade, where δ[n] is the Kronecker delta. The impulse response of the cascaded system is

Ques 63 Signals and Systems

The causal signal with z-transform z²(z-a)^-2 is (u[n] is the unit step signal)

Ques 64 Signals and Systems

Let f(t) be an even function, i.e. f(-t) = f(t) for all t. Let the Fourier transform of f(t) be defined as F(ω) = ∫_-∞^∞ f(t)e^-jωtdt for all ω, and suppose F(0) = 1. Then dF(ω) / dω = -ωF(ω) for all ω and F(0)=1.Then