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A 150 kW, 3000 V, 50 Hz, 6-pole, star-connected induction motor has a star- connected slip-ring rotor with a transformation ratio of 3-6 (stator/rotor) The rotor resistance is 012/phase and its per phase leakage inductance is 3-61 mH. The stator impedance may be neglected Find the starting torque on rated voltage with short-circuited slip rings.?
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A 150 kW, 3000 V, 50 Hz, 6-pole, star-connected induction motor has a ...
Induction Motor Specifications
- Power: 150 kW
- Voltage: 3000 V
- Frequency: 50 Hz
- Number of Poles: 6
- Connection: Star-connected
- Rotor Type: Slip-ring rotor (star-connected)
- Transformation Ratio: 3-6 (stator/rotor)
- Rotor Resistance: 0.12 Ω/phase
- Leakage Inductance: 3.61 mH
Starting Torque Calculation
To find the starting torque of the induction motor with short-circuited slip rings, we follow these steps:
1. Determining Rotor Current:
At starting, the slip (s) is 1. The rotor current can be calculated using the transformation ratio:
- \( V_{r} = \frac{V_{s}}{Transformation\ Ratio} = \frac{3000}{3} = 1000 \ V \)
2. Calculating Rotor Impedance:
The per-phase rotor impedance (Z_r) is given by:
- \( Z_{r} = R_{r} + jX_{r} \)
Where \( X_{r} = 2\pi f L_{r} \)
- \( L_{r} = 3.61 \ mH = 3.61 \times 10^{-3} \ H \)
- \( X_{r} = 2 \pi (50)(3.61 \times 10^{-3}) \approx 1.13 \ \Omega \)
- Hence, \( Z_{r} = 0.12 + j1.13 \)
3. Calculating Rotor Current (I_r):
- \( I_{r} = \frac{V_{r}}{Z_{r}} \)
- Magnitude:
- \( |Z_{r}| = \sqrt{(0.12)^{2} + (1.13)^{2}} \approx 1.13 \ \Omega \)
- \( I_{r} = \frac{1000}{1.13} \approx 885.0 \ A \)
4. Calculating Starting Torque (T_start):
Using the formula:
- \( T_{start} = \frac{3 \cdot V_{r} \cdot I_{r}}{\omega_s} \)
- Where \( \omega_s = \frac{2\pi f}{P} \)
- \( \omega_s = \frac{2\pi (50)}{6} \approx 15.71 \ rad/s \)
- Finally, substituting values gives:
- \( T_{start} = \frac{3 \cdot 1000 \cdot 885}{15.71} \approx 168,000 \ N \cdot m \)
Conclusion
The starting torque with short-circuited slip rings at rated voltage is approximately 168,000 N·m. This high torque ensures the motor can overcome static friction and start efficiently.
- Power: 150 kW
- Voltage: 3000 V
- Frequency: 50 Hz
- Number of Poles: 6
- Connection: Star-connected
- Rotor Type: Slip-ring rotor (star-connected)
- Transformation Ratio: 3-6 (stator/rotor)
- Rotor Resistance: 0.12 Ω/phase
- Leakage Inductance: 3.61 mH
Starting Torque Calculation
To find the starting torque of the induction motor with short-circuited slip rings, we follow these steps:
1. Determining Rotor Current:
At starting, the slip (s) is 1. The rotor current can be calculated using the transformation ratio:
- \( V_{r} = \frac{V_{s}}{Transformation\ Ratio} = \frac{3000}{3} = 1000 \ V \)
2. Calculating Rotor Impedance:
The per-phase rotor impedance (Z_r) is given by:
- \( Z_{r} = R_{r} + jX_{r} \)
Where \( X_{r} = 2\pi f L_{r} \)
- \( L_{r} = 3.61 \ mH = 3.61 \times 10^{-3} \ H \)
- \( X_{r} = 2 \pi (50)(3.61 \times 10^{-3}) \approx 1.13 \ \Omega \)
- Hence, \( Z_{r} = 0.12 + j1.13 \)
3. Calculating Rotor Current (I_r):
- \( I_{r} = \frac{V_{r}}{Z_{r}} \)
- Magnitude:
- \( |Z_{r}| = \sqrt{(0.12)^{2} + (1.13)^{2}} \approx 1.13 \ \Omega \)
- \( I_{r} = \frac{1000}{1.13} \approx 885.0 \ A \)
4. Calculating Starting Torque (T_start):
Using the formula:
- \( T_{start} = \frac{3 \cdot V_{r} \cdot I_{r}}{\omega_s} \)
- Where \( \omega_s = \frac{2\pi f}{P} \)
- \( \omega_s = \frac{2\pi (50)}{6} \approx 15.71 \ rad/s \)
- Finally, substituting values gives:
- \( T_{start} = \frac{3 \cdot 1000 \cdot 885}{15.71} \approx 168,000 \ N \cdot m \)
Conclusion
The starting torque with short-circuited slip rings at rated voltage is approximately 168,000 N·m. This high torque ensures the motor can overcome static friction and start efficiently.
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A 150 kW, 3000 V, 50 Hz, 6-pole, star-connected induction motor has a star- connected slip-ring rotor with a transformation ratio of 3-6 (stator/rotor) The rotor resistance is 012/phase and its per phase leakage inductance is 3-61 mH. The stator impedance may be neglected Find the starting torque on rated voltage with short-circuited slip rings.?
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A 150 kW, 3000 V, 50 Hz, 6-pole, star-connected induction motor has a star- connected slip-ring rotor with a transformation ratio of 3-6 (stator/rotor) The rotor resistance is 012/phase and its per phase leakage inductance is 3-61 mH. The stator impedance may be neglected Find the starting torque on rated voltage with short-circuited slip rings.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A 150 kW, 3000 V, 50 Hz, 6-pole, star-connected induction motor has a star- connected slip-ring rotor with a transformation ratio of 3-6 (stator/rotor) The rotor resistance is 012/phase and its per phase leakage inductance is 3-61 mH. The stator impedance may be neglected Find the starting torque on rated voltage with short-circuited slip rings.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 150 kW, 3000 V, 50 Hz, 6-pole, star-connected induction motor has a star- connected slip-ring rotor with a transformation ratio of 3-6 (stator/rotor) The rotor resistance is 012/phase and its per phase leakage inductance is 3-61 mH. The stator impedance may be neglected Find the starting torque on rated voltage with short-circuited slip rings.?.
A 150 kW, 3000 V, 50 Hz, 6-pole, star-connected induction motor has a star- connected slip-ring rotor with a transformation ratio of 3-6 (stator/rotor) The rotor resistance is 012/phase and its per phase leakage inductance is 3-61 mH. The stator impedance may be neglected Find the starting torque on rated voltage with short-circuited slip rings.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A 150 kW, 3000 V, 50 Hz, 6-pole, star-connected induction motor has a star- connected slip-ring rotor with a transformation ratio of 3-6 (stator/rotor) The rotor resistance is 012/phase and its per phase leakage inductance is 3-61 mH. The stator impedance may be neglected Find the starting torque on rated voltage with short-circuited slip rings.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 150 kW, 3000 V, 50 Hz, 6-pole, star-connected induction motor has a star- connected slip-ring rotor with a transformation ratio of 3-6 (stator/rotor) The rotor resistance is 012/phase and its per phase leakage inductance is 3-61 mH. The stator impedance may be neglected Find the starting torque on rated voltage with short-circuited slip rings.?.
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