In order to really understand how to calculate the power factor or efficiency of any motor you must understand the difference between true power or output power and apparent power or input power.
True Power = Output Power or the power that is used by the motor to do useful work.
Apparent Power = Input Power or power that is supplied to the motor but has no ability to do useful work independent of the motor.
Next you’ll need to know the difference between the way power operates in an ideal vs a practical motor.
An ideal motor is 100% efficient. Every volt-amp of power supplied to the motor (input power) is converted to watts or power that actually does useful work (output power). There is no power or energy loss as electrical energy supplied in the form of emf (electromotive force) or input power is converted to mechanical energy or output power. There is 100% efficiency in the conversion of input to output power.
A practical motor is less than 100% efficient. Every volt-amp of power supplied to the motor (input power) is not converted to watts or power that actually does useful work (output power). There is loss or waste as electrical energy supplied in the form of emf (electromotive force) or input power is converted to mechanical energy or output power.
The ratio of true power (output power) to apparent power (input power) equals the efficiency of the motor.
Calculate True Power:
Since 1 hp is equal to 746 watts multiplying the horse power of a motor by 746 watts will yield true power whether the system in question is single or three phase:
True Power (Output Power) = 746 watts x Hp Rating
Calculate Apparent Power:
There are two variations of this formula. Which one you use depends on whether the motor is single or three phase.
Single-Phase Apparent Power (Input Power) = E x I (Voltage x Current)
Three-Phase Apparent Power (Input Power) = E x I x 1.732 (Voltage x Current x 1.732)
Calculate Motor Efficiency:
What is the efficiency of a 5 hp. 230 volt single-phase A.C. motor with a f.l.c. of 28 amps?
True Power = 5 hp x 746 watts = 3,730 watts
Apparent Power = 230 volts x 28 amps = 6440 volt-amps
Efficiency = 3,730 watts/6440 volt-amps = .579 or 57.9%
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