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