GATE EE 2018 Question Paper (10-Feb-2018) (Shift 2)

The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are j0.1 pu, j0.05 pu and j0.01 pu respectively on the machine rating base. The machine is unloaded and working at the rated terminal voltage. If the grounding impedance of the generator is j0.01 pu, then the magnitude of fault current for a b-phase to ground fault (in kA) is __________ (up to 2 decimal places).

A 1000 × 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are _____ (up to 2 decimal places).

The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If I₀ = 20 A, the rms value of fundamental component of the current is ___________A (up to 2 decimal places).

A separately excited dc motor has an armature resistance Rₐ = 0.05 Ω. The field excitation is kept constant. At an armature voltage of 100 V, the motor produces a torque of 500 Nm at zero speed. Neglecting all mechanical losses, the no-load speed of the motor (in radian/s) for an armature voltage of 150 V is _____ (up to 2 decimal places).

Consider a unity feedback system with forward transfer function given by

$G\left(S\right)=\frac{1}{\left(s+1\right)\left(s+2\right)}$

The steady-state error in the output of the system for a unit-step input is _________ (up to 2 decimal places).