Q5Electrical Machine Design

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Q.5. A 3-φ induction motor has 54 slots with 8 conductors per slot and 72 rotor slots with 4 conductors per slot. Find the number of stator and rotor turns. Find voltage across the rotor slip-rings, when the rotor is open circuited at rest. Both stator and rotor are star connected and a voltage of 400 volts is applied across the stator terminals.

Answer 1

Given data: 3-phase induction motor, stator: 54 slots, 8 conductors/slot; rotor: 72 slots, 4 conductors/slot; both stator and rotor star-connected; stator line voltage = 400V.

Step 1 — Stator turns per phase: total stator conductors = 54×8 = 432. For a 3-phase winding, conductors per phase = 432/3 = 144. Since 2 conductors form 1 turn:

T_{s t a t or} = \frac{144}{2} = 72 turns/phase

Step 2 — Rotor turns per phase: total rotor conductors = 72×4 = 288. Conductors per phase = 288/3 = 96. Turns per phase:

T_{r o t or} = \frac{96}{2} = 48 turns/phase

Step 3 — Stator phase voltage (star connection):

V_{s t a t or, p ha se} = \frac{400}{3} \approx 230.9 V

Step 4 — Turns ratio and rotor phase voltage (transformer-like relationship at standstill, rotor open-circuited):

\frac{T _{s t a t or}}{T _{r o t or}} = \frac{72}{48} = 1.5

V_{r o t or, p ha se} = \frac{V _{s t a t or, p ha se}}{1.5} = \frac{230.9}{1.5} \approx 153.96 V

Step 5 — Rotor slip-ring (line) voltage, since rotor is star-connected:

V_{r o t or, l in e} = 3 \times V_{r o t or, p ha se} = 1.732 \times 153.96 \approx 266.7 V

Therefore, the rotor has 48 turns per phase, and the voltage appearing across the open-circuited rotor slip-rings at standstill (rest) is approximately 266.7V, when 400V is applied across the star-connected stator terminals — this calculation directly parallels the transformer turns-ratio and voltage relationship, treating the induction motor's stator and rotor as the primary and secondary of a rotary transformer at the standstill (zero-slip-frequency-independent) condition.

This open-circuit slip-ring voltage value is an important practical design output, since it directly determines the voltage rating (and hence insulation level) required for the slip rings, brushes, and any external rotor starting resistance or control equipment connected to the wound rotor circuit, and is typically kept to a moderate value (as it is here, at under 300V) specifically to keep this external rotor equipment's insulation and safety requirements economical and straightforward, compared to what would be needed if a much higher slip-ring voltage were allowed to result from an unconstrained turns-ratio design choice. The same turns-ratio arithmetic also fixes the rotor current scale relative to the stator (rotor current being approximately the stator current multiplied by the 1.5 turns ratio), which is the companion calculation a designer performs immediately after this voltage determination to size the rotor conductors, slip rings, and brushes for the wound-rotor circuit.

Q5Electrical Machine Design

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