Question

A 1100V, 50Hz Δ-connected induction motor has a star-connected slip-ring rotor with a phase transformation ratio of 3.8. The rotor resistance and standstill leakage reactance are 0.012 ohm and 0.25 ohm per phase, respectively. Neglecting stator impedance and magnetizing current, determine: (i) Rotor current at start with slip-rings shorted a) 0 A b) 100 A c) 200 A d) 300 A

Answer 1

The rotor current at start with the slip-rings shorted is 300A.

Step-by-step explanation:

To determine the rotor current at start with the slip-rings shorted, we can use the equivalent circuit model of an induction motor. The rotor current can be calculated using the formula:

Stator Line Voltage / Rotor Impedance at Start

Given that the stator line voltage is 1100V and the rotor impedance at start is the sum of the rotor resistance and standstill leakage reactance, we can substitute the values into the formula:

Rotor current at start = 1100V / (Rotor Resistance + Standstill Leakage Reactance)

= 1100V / (0.012 ohm + 0.25 ohm)

= 1100V / 0.262 ohm

= 4198A

Therefore, the correct option is d) 300A.

Answer 2

To find the rotor current at start with slip-rings shorted, one must calculate the equivalent stator parameters using the transformation ratio, determine stator voltage per phase from the line voltage, and apply Ohm's law using the transformed rotor resistance and reactance for a stator-referenced phase at startup.

Step-by-step explanation:

To determine the rotor current at start with slip-rings shorted for the given Δ-connected induction motor, we must consider that the rotor is at a standstill at startup or the slip s=1. We can use the transformation ratio to convert the rotor parameters to equivalent stator parameters. Given that the transformation ratio is 3.8, the rotor resistance (R'2) and standstill leakage reactance (X'2) per phase on a stator basis would be R'2 = rotor resistance × (transformation ratio)^2 and X'2 = standstill leakage reactance × (transformation ratio)^2, respectively. Then the stator voltage per phase (Vstator_phase) for a Δ-connection would be Vstator_phase = Vline / √3. Now, we can calculate the startup rotor current (I2_start) using Ohm's law for a stator-referenced phase:

Vstator_phase = √(R'2^2 + (s × X'2)^2) × I2_start

where s=1 at startup. After simplifying and solving this equation, we can determine the approximate value of the rotor current from the provided options (a to d).