GATE 2023 EE Q.15: solution and answer

GATE 2023 · EEQ.15 · 1 mark · MCQ

The following columns present various modes of induction machine operation and the ranges of slip.

Column A (Mode of operation): a. Running in generator mode b. Running in motor mode c. Plugging in motor mode
Column B (Range of Slip): p) From 0.0 to 1.0 q) From 1.0 to 2.0 r) From -1.0 to 0.0

The correct matching between the elements in column A with those of column B is

(A)
a-r, b-p, and c-q
(B)
a-r, b-q, and c-p
(C)
a-p, b-r, and c-q
(D)
a-q, b-p, and c-r

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Answer and solution

ANSWER

The correct matching is a-r, b-p, and c-q — option A.

Official answer: ASource: Official answer key, GATE 2023 EE (IIT Kanpur)

Slip is defined as $s = \frac{N _{s} - N _{r}}{N _{s}}$ , where $N_{s}$ is the synchronous speed of the stator's rotating field and $N_{r}$ is the rotor speed, both measured in the same reference direction.
Motoring mode: the rotor rotates in the same direction as the field but below synchronous speed, so $0 < N_{r} < N_{s}$ , giving $0 < s < 1$ . This is range (p), "From 0.0 to 1.0" — so b-p.
Generator mode: an external prime mover drives the rotor above synchronous speed in the same direction as the field, so $N_{r} > N_{s}$ , making the slip negative. The conventionally quoted slip range for this mode is "From $- 1.0$ to $0.0$ " — range (r) — so a-r.
Plugging (braking) mode: interchanging two of the three stator supply leads reverses the direction of the rotating field, while the rotor (by inertia) keeps turning in its original direction. Relative to the new field direction, the rotor's speed is effectively $- N_{r}$ , so $s = \frac{N _{s} - ( - N _{r} )}{N _{s}} = 1 + \frac{N _{r}}{N _{s}}$ .
Just after plugging, $N_{r}$ is close to the pre-plugging running speed (near $N_{s}$ ), so $s \to 2$ ; as the rotor slows toward standstill, $N_{r} \to 0$ and $s \to 1$ . Hence slip ranges from $1.0$ to $2.0$ — range (q) — so c-q.
Combining: a-r (generator), b-p (motor), c-q (plugging), which is option (A).

KEY IDEA

Slip $s = \frac{N _{s} - N _{r}}{N _{s}}$ takes different ranges depending on the relative direction and speed of the rotor with respect to the (possibly reversed) rotating field: $0$ to $1$ in motoring, negative in generating (rotor driven faster than sync speed, same direction as the field), and above $1$ (up to $2$ ) in plugging, where reversing two supply leads reverses the field direction while the rotor keeps turning the old way.

WATCH OUT FOR

Confusing the sign convention: assuming plugging gives a negative slip (like generator action) instead of realizing that reversing two supply leads reverses the direction of the rotating field, so the rotor's own direction becomes "backward" relative to the new field, pushing slip past 1 (up to 2) rather than below 0.

From the GATE 2023 EE paper. Every question of this paper · Download the full paper · All 17 Induction machines questions, with notes

GATE 2023 EE Q.15: solution and answer

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