Power & Torque
The input power to a three-phase induction machine is given by
Output power can be found by subtracting the losses from the input power
- Stator Copper Loss. The stator resistive losses
- Rotor Joule Loss. The rotor resistive losses. This is often called rotor copper loss, but since the
rotor conductors are aluminum, rotor joule loss is the more correct terminology.
- Core Loss, or Iron Loss. The losses due to eddy current and hysteresis losses in the laminations. This can be calculated using the resistor Rc. Often, core losses are grouped with friction and windage and stray loss as rotational losses.
The power transferred to the rotor is called the "Airgap Power". Consider the equivalent circuit below (the core loss resistance has been removed and core losses grouped into rotational loss).
From the above circuit, it can be seen that the total power transfer to the rotor is given by
To find the power converted to the mechanical system the rotor joule loss must be subtracted from the total rotor power
From the above equations, it can be seen that power converters to the mechanical system is a function of the airgap power and slip:
Final output power may be obtained by subtracting the rotational loss from Pconv.
As with all rotating mechanical systems in steady state, torque can be found from the power and mechanical speed
In the case of an induction machine, the electromagnetic torque generated by the machine can be found using
Writing the torque in terms of the rotor current:
Finally, to find the available shaft torque after rotational losses, the output power must be used.