GATE EE 2014 Question Paper (02-Mar-2014) (Shift 2)

For a 400 km long transmission line, the series impedance is (0.0 + j 0.5) Ω / km and the shunt admittance is (0.0 + j 5.0) μmho/km. The magnitude of the series impedance (in Ω) of the equivalent π circuit of the transmission line is_________.

The complex power consumed by a constant – voltage load is given by (P₁ + jQ₁), Where, 1 kW ≤ P₁ ≤ 1.5 kW and 0.5 kVAR ≤ Q₁ ≤ 1 kVAR.

A compensating shunt capacitor is chosen such that |Q| ≤ 0.25 kVAR, where Q is the net reactive power consumed by the capacitor – load combination. The reactive power (in kVAR) supplied by the capacitor is__________.

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 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 P${}_{max}$

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 P${}_{max}$ (in pu) is___________.

The block diagram of a system is shown in the figure.



If the desired transfer function of the system is

$\frac{C\left(s\right)}{R\left(s\right)}=\frac{s}{s^2+s+2}$

then G(s) is

Consider the system described by following state space equations

≤ft[ {*20c {x_1}\\ {x_2} } ] = ≤ft[ {*20c 0&1\\ - 1& - 1 } ]≤ft[ {*20c x_1\\ x_2 } ] + ≤ft[ {*20c 0\\ 1 } ]u;y = ≤ft[ {*20c 1&0 } ]≤ft[ {*20c x_1\\ x_2 } ]

If u is unit step input, then the steady state error of the system is