1
GATE EE 2022
+1
-0.33

The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by

Plant 1 : C1 = 350 + 6P1 + 0.004P$$_1^2$$

Plant 2 : C2 = 450 + aP2 + 0.003P$$_2^2$$

where P1 and P2 are power generated by plant 1 and plant 2, respectively, in MW and a is constant. The incremental cost of power ($$\lambda$$) is 8 rupees per MWh. The two thermal power plants together meet a total power demand of 550 MW. The optimal generation of plant 1 and plant 2 in MW, respectively, are

A
200, 350
B
250, 300
C
325, 225
D
350, 200
2
GATE EE 2022
Numerical
+1
-0.33

Two generating units rated for 250 MW and 400 MW have governor speed regulations of 6% and 6.4%, respectively, from no load to full load. Both the generating units are operating in parallel to share a load of 500 MW. Assuming free governor action, the load shared in MW, by the 250 MW generating unit is ________. (round off to nearest integer).

3
GATE EE 2022
Numerical
+1
-0.33

A 20 MVA, 11.2 kV, 4-pole, 50 Hz alternator has an inertia constant of 15 MJ/MVA. If the input and output powers of the alternator are 15 MW and 10 MW, respectively, the angular acceleration in mechanical degree/s2 is _________. (round off to nearest integer).

4
GATE EE 2022
+1
-0.33

Let a causal LTI system be governed by the following differential equation $$y(t) + {1 \over 4}{{dy} \over {dt}} = 2x(t)$$, where x(t) and y(t) are the input and output respectively. Its impulse response is

A
$$2{e^{ - {1 \over 4}t}}u(t)$$
B
$$2{e^{ - 4t}}u(t)$$
C
$$8{e^{ - {1 \over 4}t}}u(t)$$
D
$$8{e^{ - 4t}}u(t)$$
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