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The rotor resistance and standstill reactance of a 3-phase induction motor are respectively 0.015 Ω and 0.09 Ω per phase. At normal voltage the full-load slip is 3%. Ignore stator impedances. Estimate the percentage reduction in stator voltage to develop full-load torque at one-half of full load speed. What will be the power factor?
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The rotor resistance and standstill reactance of a 3-phase induction m...
Estimation of Stator Voltage Reduction and Power Factor in a 3-Phase Induction Motor


Given Parameters:


  • Rotor resistance per phase: 0.015 Ω

  • Standstill reactance per phase: 0.09 Ω

  • Full-load slip: 3%



Calculation of Full-load Torque:

Full-load torque is given by the formula:

TFL = (3 x V12 / 2πf) x (R2 / s) / (R2 / s)2 + (X2 + X1)2

where,


  • V1 = Normal voltage

  • f = Frequency

  • R2 = Rotor resistance per phase

  • s = Full-load slip

  • X2 = Standstill reactance per phase

  • X1 = Stator reactance per phase (Assumed to be zero)


Substituting the given values, we get:

TFL = (3 x V12 / 2πf) x (0.015 / 0.03) / (0.015 / 0.03)2 + (0.09)2 = 0.039 V12 / f


Calculation of Stator Voltage Reduction:

Stator voltage reduction to develop full-load torque at one-half of full load speed is given by the formula:

V2 / V1 = (1 - s / 2) / (1 - 2s / 3)

where,


  • V2 = Reduced stator voltage

  • V1 = Normal voltage

  • s = Full-load slip


Substituting the given values, we get:

V2 / V1 = (1 - 0.03 / 2) / (1 - 2 x 0.03 / 3) = 0.942

Hence, the percentage reduction in stator voltage will be:

(1 - 0.942) x 100% = 5.8%


Calculation of Power Factor:

Power factor at full-load is
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The rotor resistance and standstill reactance of a 3-phase induction motor are respectively 0.015 Ω and 0.09 Ω per phase. At normal voltage the full-load slip is 3%. Ignore stator impedances. Estimate the percentage reduction in stator voltage to develop full-load torque at one-half of full load speed. What will be the power factor?
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