Power in Motors

Power in Motors

AC motors are either single-phase or three-phase. For a single-phase motor, the electrical input power is given by Equation (A).

 (A) Pin = VIcosθ  V is the rms line voltage, I is the rms line current, and cosθ is the power factor.
 As we learned in the lesson on three-phase,

 (B) Pin = √3 VIcosθ  The output mechanical power is:

 (C) Pout = Toutωm  Pout is the output mechanical power, Tout is the output torque, and ωm is the angular frequency of the shaft.

 (D) Pin = Pout + Ploss 
Ploss refers to the copper, eddy current, hysteresis, friction, and windage losses.
Pout is usually given in horsepower (746 W/HP). The efficiency of a motor (η) is the ratio of the powers:

 (F) η = Pout/Pin
Typical values for industrial motors are between 85% and 95%. It should be understood that these efficiency are for full load. Efficiency decreases significantly for light loads.

 Since motor speeds are usually given in rpm rather than shaft angular frequency, conversion is frequently necessary:

 (G) ωm = nm(2π)/60  nm is the motor shaft rotation in rpm.