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Problem # 5-7

Problem # 5-7. A 3-phase, 8-pole, induction motor, rated at 874rpm, 30hp, 60Hz, 460V, operating at reduced load, has a shaft speed of 880 rpm . The combined stray power loss, windage loss, and friction loss is 350W. The rotor parameters in Ω/phase are R 1 =0.1891 R 2 =0.191 X M =14.18

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Problem # 5-7

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  1. Problem # 5-7 • A 3-phase, 8-pole, induction motor, rated at 874rpm, 30hp, 60Hz, 460V, operating at reduced load, has a shaft speed of 880 rpm. The combined stray power loss, windage loss, and friction loss is 350W. The rotor parameters in Ω/phase are • R1=0.1891 R2=0.191 XM=14.18 • X1=1.338 X2=0.5735 Rfe=189.1 ECE 441

  2. Equivalent Circuit for an Induction Motor with all parameters referenced to the stator ECE 441

  3. Problem # 5-7 continued • The motor is NEMA Design C and Y-connected. • Determine • the motor input impedance/phase Need to determine the value of s. ECE 441

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  6. The Input Impedance per Phase ECE 441

  7. Solution continued • Determine the line current ECE 441

  8. 3-ΦDelta and Wye Connections • (a) shows the sources (phases) connected in a wye (Y). • Notice the fourth terminal, known as Neutral. • (b) shows the sources (phases) connected in a delta (∆). • Three terminals ECE 441

  9. Solution continued • Determine the active, reactive, and apparent power and power factor ECE 441

  10. Solution continued • Determine the equivalent rotor current ECE 441

  11. Solution continued • Determine the stator copper loss ECE 441

  12. Solution continued • Determine the rotor copper loss ECE 441

  13. Solution continued • Determine the core loss ECE 441

  14. Solution continued • Determine the air gap power ECE 441

  15. Solution continued • Determine the mechanical power developed ECE 441

  16. Solution continued • Determine the developed torque ECE 441

  17. Solution continued • Determine the shaft horsepower ECE 441

  18. Solution continued • Determine the shaft torque ECE 441

  19. Solution continued • Determine the efficiency ECE 441

  20. Solution continued • Sketch the power flow diagram and enter all data 18,781.8W 18,368.6W 20,393.5W 24.33hp 631.5W 850.5W 413.2W 350W ECE 441

  21. Solution continued • Determine the expected minimum locked-rotor torque, breakdown torque, and pull-up torque • From Table 5-1, Tlr=200%Trated • Tlr = (2)(180.27) = 360.54 lb-ft • From Table 5-3, Tbreakdown = 190%Trated • Tbreakdown = (1.9)(180.27) = 342.52 lb-ft • From Table 5-6, Tpull-up = 140%Trated • Tpull-up = (1.4)(180.27) = 252.37 lb-ft ECE 441

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