1
GATE EE 1998
Subjective
+5
-0
In a power system, the fuel inputs per hour of plants $$1$$ and $$2$$ are given as
$${F_1} = 0.20\,P_1^2 + 30\,{P_1} + 100\,\,$$ Rs per hour
$${F_2} = 0.25\,P_2^2 + 40\,{P_2} + 150\,\,$$

The limits of generators are \eqalign{ & 20 \le {P_1} \le 80\,MW \cr & 40 \le {P_2} \le 200\,MW \cr}\$
Find the economic operating schedule of generation, If the load demand is $$130$$ $$MW.$$ neglecting transmission losses.

2
GATE EE 1998
+2
-0.6
The neutral of $$10$$ $$MVA,$$ $$11$$ $$kV$$ alternator is earthed through a resistance of $$5$$ ohms. The earth fault relay is set to operate at $$0.75$$ $$A.$$ The $$CT's$$ have a ratio of $$1000/5.$$ What percentage of the alternator winding is protected?
A
$$85$$%
B
$$88.2$$%
C
$$15$$%
D
$$11.8$$%
3
GATE EE 1998
+1
-0.3
Bulk power transmission over long HVDC lines are preferred, on account of
A
low cost of HVDC treminals
B
no harmonic problems
C
minimum line power losses
D
simple protection
4
GATE EE 1998
+2
-0.6
The Laplace transform of $$\left(t^2\;-\;2t\right)u\left(t\;-\;1\right)$$ is
A
$$\frac2{s^3}e^{-s}\;-\;\frac2{s^2}e^{-s}$$
B
$$\frac2{s^3}e^{-2s}\;-\;\frac2{s^2}e^{-s}$$
C
$$\frac2{s^3}e^{-s}\;-\;\frac1se^{-s}$$
D
None of the above
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