Motor efficiency formula:
Motor efficiency η is equal to the ratio between the output power P(o) in watts to input power P(i) in watts.
η = Po / Pi
Efficiency is always mentioned in percentage %
η = Po x 100 / Pi
Pi in watts is equal to the product of input voltage Vi in volts input current Ii in amps
Pi = Vi x Ii
This is the basic formula for motor efficiency calculation.
DC motor efficiency:
Let us take Motor Output = V x I
Motor Input = motor output + Loss
DC motor has three losses such as copper losses, iron losses and mechanical losses.
Hence the motor output = Input – (Copper loss + iron loss + Mechanical loss)
The motor efficiency formula become,
η = Output / (Input – (Copper loss + iron loss + Mechanical loss))
η = (V*I) / (VI – ((I2*R) + We + Wm))
Efficiency for 3 phase AC motors:
AC motor efficiency is equal to the net output at the shaft to net electrical input to the motor
% η = Net output of the shaft / net electrical input.
Here the net input P(input) in watts is equal to the 1.732 to times of the current and voltage and power factor.
P(input) = 1.732 x VL x IL x pf
The mechanical power is equal to net input electrical power P(input) minus total losses including stator copper loss, rotor copper loss and mechanical friction losses.
P(mechanical) = P(input) – (Stator loss + Rotor copper loss + mechanical loss)
Here starter copper loss = 3 x IL2 x Rstator
Here RStator is the stator resistance of the coil.
Rotor Copper loss = 3 x I2r2 x R(rotor)
Here the 3 phase motor efficiency formula can be written as,
I2r is the rotor input current in amps.
R(rotor) is the rotor resistance in ohms.
R(stator) stator coil resistance in ohms
Also, note that the maximum efficiency of the motor can be archived when the variable loss is equal to the constant loss of the motor