Induction Motor Voltage & RPM

I have hardly seen a motor nameplate has such three voltage ranges. Anyway here is your answer.

With the increase of voltage, why RPM increases?

The torque developed by the motor is directly proportional to motor terminal the voltage. In the torque-speed characteristics curve of the motor, the torque curve moved upward with the increase of voltage and the motor full load torque intersects to the torque curve at slightly right of the new elevated torque curve (see the D point of the torque-speed curve from link below), which means with the same full load torque, the motor runs at higher speed.

See http://ecmweb.com/mag/electric_understanding_induction_motor

With the increase of voltage, why Power Factor Decreases?

With higher voltage at the motor terminal, the flux density increases and hence it draws more magnetizing current (the reactive component of the current) compared to the real component of current. Higher magnetizing current component causes lower power factor.

- MS

Whatever U have calculated is the input power ( Electrical) (P in = 1.732 *V *I*P.F) to the Induction motor. Motor Nameplate mentioned power is always the Mechanical Power (Output of I M).

If we introduce efficiency to the Input Power (1.732 *V *I*P.F*Efficiency),we have Mechanical or Nameplate mentioned Power of the motor. For 380 V case efficiency is approximately 80.7 %.

"first time i have seen three rated voltages too..."

In Low KW rating ( Up to 7.5 KW) I have even seen many motors mentioning three voltages. The present motor is Water Pump Motor made by Franklin Electric and its Model no is 2366186033. If U doesn't agree I even gave more examples if U wish

Mmmm!

Note:
Power factor improves with lower voltage and drops sharply with high voltage.Now see the below picture