An AC motor is a transformer? How?

Question

motivation:
A guy I worked with years ago (~2015) who is an EE said that "an electric motor was just another form of a transformer". I'm not an EE, so I didn't do things with transformers. I think he meant that it turns energy from one form into another, but that he also meant there was a mathematical parallel in the modeling. Maybe something presuming steady-state, not accounting for spin-up of the armature?

Note: he loved 3-phase, for what that is worth.

Question:
Can you show the basic circuit and mathematical model of a simple electrical transformer, and then show a simple model for an equivalent electrical motor. Ideally there should be some python (numpy/scipy) with an ODE45 and a graph of current, voltage, accounting for windings, and somehow relating that to motor rotation or something.

Showing my homework:
I tried searching this forum and found no result that seemed to answer the question.

Links:

• https://www.electricaltechnology.org/2019/10/difference-between-transformer-induction-motor.html (while it talks about features and differences, it doesnt give me enough to understand the idea of model similarity.)
• https://www.tutorialspoint.com/difference-between-induction-motor-and-transformer (words, but not models)
• https://www.idc-online.com/technical_references/pdfs/electrical_engineering/Fundamentals_of_Electric_Motors_and_Transformers.pdf (good fundamental and vocab, but not a way to connect via a model)
• Is it possible to model a single-phase phase-shifting transformer in LTspice/Multisim/PSpice?

Answer 1

You'd want to start with a reference book on electrical machines. It'll have the state equations to get you going.

The simplest form of a "motor transformer" is a two-phase stepper or BLDC motor. Apply a sine wave close to the electromechanical resonance frequency to phase 1 winding. Lock the rotor. Phase 2 winding will output "close to nothing". Now unlock the rotor. Phase 2 winding will output a phase-shifted version of the input to phase 1.

Compared to a regular transformer, there's additional phase shift due to rotor slip angle. The motor acts just like a 1:1 transformer would, less phase shift, with two additional transductions in series with energy flow: magnetic to mechanical on phase 1 ("primary"), and mechanical to magnetic on phase 2 ("secondary").

A BLDC/stepper with stator poles 180 electrical degrees apart will work very similarly to a 1:1 transformer.

A three-phase induction motor works similarly, except that the rotor magnetic field is due to current flow in the cage, induced by the stator.