1
GATE EE 2008
+2
-0.6
A lossless power system has to serve a load of $$250$$ $$MW.$$ There are two generators ($$G1$$ and $$G2$$) in the system with cost curves $${C_1}$$ and $${C_2}$$ respectively defined as follows:
$${C_1}\left( {{P_{G1}}} \right) = {P_{G1}} + 0.055 \times P_{G1}^2$$
$${C_2}\left( {{P_{G2}}} \right) = 3{P_{G2}} + 0.03 \times P_{G2}^2$$
Where $${P_{G1}}$$ and $${P_{G2}}$$ are the MW injections from generator $${G_1}$$ and $${G_2}$$ respectively. Thus, the minimum cost dispatch will be
A
$${P_{G1}} = 250\,MW;\,\,{P_{G2}} = 0\,MW$$
B
$${P_{G1}} = 150\,MW;\,\,{P_{G2}} = 100\,MW$$
C
$${P_{G1}} = 100\,MW;\,\,{P_{G2}} = 150\,MW$$
D
$${P_{G1}} = 0\,MW;\,\,{P_{G2}} = 250\,MW$$
2
GATE EE 2008
+1
-0.3
A two machine power system in shown below. Transmission line $$XY$$ has positive sequence impedance of $${Z_1}\Omega$$ and zero sequence impedance of $${Z_0}\Omega$$
An $$'a'$$ phase to ground fault with zero fault impedance occurs at the centre of the transmission line. Bus voltage at $$X$$ and line current from $$X$$ to $$F$$ for the phase $$'a',$$ are given by $${V_a}$$ Volts and $${{\rm I}_a}$$ Amperes, respectively. Then, the impedance measured by the ground distance relay located at the terminal $$X$$ of line $$XY$$ will be given by
A
$${Z_1}/2\Omega$$
B
$${Z_0}/2\Omega$$
C
$$\left( {{Z_0} + {Z_1}} \right)/2\Omega$$
D
$${V_a}/{{\rm I}_a}\,\Omega$$
3
GATE EE 2008
+2
-0.6
Voltage phasors at the two terminals of a transmission line of length $$70$$ km have a magnitude of $$1.0$$ per unit but are $$180$$ degrees out of phase. Assuming that the maximum load current in the line is $$1/5$$th of minimum $$3$$-phase fault current. Which one of the following transmission line protection schemes will NOT pick up for this condition?
A
Distance protection using mho relays with zone-$$1$$ set to $$80$$% of the line impedance.
B
Directional over current protection set to pick up at $$1.25$$ times the maximum load current
C
Pilot relaying system with directional comparison scheme
D
Pilot relaying system with segregated phase comparison scheme.
4
GATE EE 2008
+2
-0.6
Let x(t) be a periodic signal with time period T. Let y(t) = x(t - t0) + x(t + t0) for some t0. The Fourier Series coefficient of y(t) are denoted by bk. If bk=0 for all odd k, then t0 can be equal to
A
T/8
B
T/4
C
T/2
D
2T
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