3 Phase Motor Efficiency Formula & DC motor Efficiency Calculation

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 = P_o / P_i

Efficiency is always mentioned in percentage %

η = P_o x 100 / P_i

P_i in watts is equal to the product of input voltage V_i in volts input current I_i in amps

P_i = V_i x I_i

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) + W_e + W_m))

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 V_L x I_L 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 I_L² x R_stator

Here RStator is the stator resistance of the coil.

Rotor Copper loss = 3 x I_2r² 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