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Power Factor Correction

Power Factor Correction. Example 8.3 page 324 of the text by Hubert A three-phase (y-connected) 60-Hz, 460-V system supplies the following loads: 6-pole, 60-Hz, 400-hp induction motor at ¾ load with an efficiency of 95.8% and power factor of 89.1% 50-kW delta-connected resistance heater

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Power Factor Correction

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  1. Power Factor Correction • Example 8.3 page 324 of the text by Hubert • A three-phase (y-connected) 60-Hz, 460-V system supplies the following loads: • 6-pole, 60-Hz, 400-hp induction motor at ¾ load with an efficiency of 95.8% and power factor of 89.1% • 50-kW delta-connected resistance heater • 300-hp, 60-Hz, 4-pole, synchronous motor at ½ load with a torque angle of -16.4.

  2. Power Factor Correction 6-pole, 60-Hz, 400-hp induction motor ¾ rated load efficiency = 95.8% power factor = 89.1% 50-kW resistance heater 4-pole,60-Hz, 300-hp cylindrical synchronous motor ½ rated load torque angle = -16.4

  3. (a) System Active Power • Induction Motor

  4. System Active Power (continued) • Heater

  5. System Active Power (continued) • Synchronous Motor

  6. System Active Power (continued)

  7. (b) Power Factor of the Synchronous Motor • Determine the angle between VT and Ia • Calculate Pin to determine Ef • Calculate Ia

  8. (c) System Power Factor • Look at each load • Induction Motor • Fp = 0.891 • θ = cos-1(0.891) = 27 • Heater • θ = 0 • Synchronous Motor • θ = -34.06

  9. Look at the Power Triangles • Induction Motor Qindmtr = Ptanθ Qindmot = 119,031.1 VARS S θ = 27 Pindmot = 233,611.7 W

  10. Power Triangles (continued) • Synchronous Motor • Heater Psynmot = 116,562.5 W θ = -34.06 Qsynmot = Ptanθ Qsynmot = -78,800 VARS Pheater = 50,000 W

  11. Adding Components

  12. Resultant • System Power Triangle θ = tan-1(40,231.1/400,200) θ = 5.74 Qsystem = 40,231.1 VARS θ = 5.74 Psystem = 400.2 kW Fp,sys = cos(5.74) = 0.995 lagging

  13. (d) Adjust power Factor to Unity • Power Triangle for the Synchronous Motor Psynmot = 116,562.5 W Qsyn mot = (78,800 + 40,231.1) VARS Ssynmot = 166,598.98-45.6 additional VARS provided by the synchronous motor

  14. For one phase

  15. Rotor Circuit for one phase

  16. Rotor Circuit for one phase (cont) • Neglecting saturation, • Ef Φf  If use Ef • ΔEf = (378.04 – 345.615)/(345.615) x 100% • ΔEf = 9.38%

  17. (e) The power angle for unity power factor • δ = -14.96

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