A 3-phase star connected slip ring induction motor has the following parameters referred to the stator: \[ R_s = 3 \, \Omega, \, X_s = 2 \, \Omega, \, X_r' = 2 \, \Omega, \, R_r' = 2.5 \, \Omega \] The per phase stator to rotor effective turns ratio is 3:1. The rotor winding is also star connected. The magnetizing reactance and core loss of the motor can be neglected. To have maximum torque at starting, the value of the extra resistance in ohms (referred to the rotor side) to be connected in series with each phase of the rotor winding is ___________ (rounded off to 2 decimal places).
A 3-phase star connected slip ring induction motor has the following parameters referred to the stator: \[ R_s = 3 \, \Omega, \, X_s = 2 \, \Omega, \, X_r' = 2 \, \Omega, \, R_r' = 2.5 \, \Omega \] The per phase stator to rotor effective turns ratio is 3:1. The rotor winding is also star connected. The magnetizing reactance and core loss of the motor can be neglected. To have maximum torque at starting, the value of the extra resistance in ohms (referred to the rotor side) to be connected in series with each phase of the rotor winding is ___________ (rounded off to 2 decimal places).
Show Hint
Correct Answer: 0.277
Solution and Explanation
Step 1: Condition for maximum starting torque
For maximum torque at starting, the total rotor resistance must equal the rotor reactance:
\[ R_2' + R_{\text{ext}} = X_2' \]
Step 2: Compute equivalent rotor impedance term
Given:
\[ \frac{R_2'}{s} = \sqrt{R_1^2 + (x_1 + x_2)^2} \]
\[ = \sqrt{9 + 16} = \sqrt{25} = 5 \]
Thus,
\[ \frac{R_2'}{s} = 5 \]
Step 3: Apply starting condition
For starting,
\[ s = 1 \]
Hence,
\[ R_2' + R_{\text{ext}} = 5 \]
Given rotor resistance:
\[ R_2' = 2.5\ \Omega \]
Therefore,
\[ R_{\text{ext}} = 5 - 2.5 = 2.5\ \Omega \]
Step 4: Refer external resistance to rotor side
External resistance referred to rotor side is:
\[ R_{\text{ext (referred)}} = \left(\frac{1}{3}\right)^2 R_{\text{ext}} \]
\[ = \frac{1}{9} \times 2.5 = 0.277\ \Omega \]
Final Answer:
External resistance referred to rotor side = 0.277 Ω
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