GATE 2022 EE Q.57: solution and answer

GATE 2022 · EEQ.57 · 2 marks · NAT

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/s^2 is __________. (round off to nearest integer)

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Answer and solution

ANSWER

The angular acceleration of the rotor is 75 mechanical degree/s^2.

Official answer: 74 to 76Source: Official answer key, GATE 2022 EE (IIT Kharagpur)

Accelerating power (losses neglected, since only input and output powers are given): $P_{a} = P_{in} - P_{o u t} = 15 - 10 = 5 MW$ .
Stored kinetic energy at synchronous speed: $G H = 20 MVA \times 15 MJ/MVA = 300 MJ$ .
Swing equation with $δ$ in electrical degrees: $\frac{G H}{180 f} \frac{d ^{2} δ}{d t ^{2}} = P_{a}$ .
Electrical angular acceleration: $\frac{d ^{2} δ}{d t ^{2}} = \frac{180 f P _{a}}{G H} = \frac{180 \times 50 \times 5}{300} = 150 elec. degree/s^{2}$ .
For a 4-pole machine, $θ_{e l ec} = \frac{P}{2} θ_{m ec h} = 2 θ_{m ec h}$ , so the mechanical acceleration is half the electrical one.
Mechanical angular acceleration: $\frac{150}{2} = 75 mech. degree/s^{2}$ .

KEY IDEA

The swing equation gives the acceleration in electrical degrees, $\frac{180 f P _{a}}{G H}$ . Divide by the number of pole pairs, $P /2$ , to convert it to mechanical degrees.

WATCH OUT FOR

Leaving the answer as 150, which is the electrical acceleration. The question asks for mechanical degrees, so divide by the number of pole pairs. Another slip is using H in MJ/MVA without multiplying by the 20 MVA rating.

From the GATE 2022 EE paper. Every question of this paper · Download the full paper · All 4 Stability questions, with notes

GATE 2022 EE Q.57: solution and answer

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