Before developing a behavioral model, you must clearly identify the purpose and constraints of the model. How much accuracy do you want and how long are you willing to wait for it?

The most accurate way to model the motor is to model each of the three phases individually and use detailed models of the drive electronics. However, the switching frequency of the drive system will probably tax your patience. There is also the trigonometric operations on the shaft angle. Since the shaft spins at a high rate compared to the time constants of interest, the shaft rotation also slows the simulation.

In any motor model, an ideal transformer converts winding current to shaft torque in one direction while converting shaft velocity to back emf in the other. Each winding has such a transformer and the turns ratio depends dynamically on shaft angle. The shaft angle comes from integrating shaft velocity. One way to think of this system is as a PLL. The shaft  converts speed to positiion the same way a VCO converts frequency to phase.

The first simplification (i.e. way to reduce run time), in my opinion, is to use state space averaged models for the power electronics. The next level of simplification is to assume unilateral signal flow from the drive to the winding. In other words, if you are controlling winding current, you may be able to neglect the effects of the winding impedance and back emf.

If after using state space averaged models for the power electronics your patience is still taxed, you can perform two transformations on the motor variables to remove the trigonometric functions of shaft angle in the ideal transformers that convert current to torque. The first transformation is from 3-phase motor to an equivalent 2-phase motor. The second transformation converts stator variables to rotor variables. In the rotor reference frame, the transformer turns ratios are constant; they no longer depend on trigonometric functions of shaft angle. This model is particularly simple if you treat the power electronics as ideal current sources.

As you look upstream in the power electronics, you must eventually assume power comes from an ideal source. The further away from the shaft you make that assumption, the more accurate your model. You can use the aforementioned transformation to the rotor reference frame and still include mechanical loading on the power electronics through the back emf by also transforming the drive electronics to the rotor reference frame. The overall model runs fast because state space averaging removes the switching frequency and the rotor-referenced variables remove dependencies on shaft angle. The down side is that all of the inductors and capacitors in one phase of the drive electronics are coupled through controlled sources to their counterparts in the other phase. If you are interested, I can dig up a paper for you.

Jess,

  How good are the models with trignometric
approximations at capturing start-up effects?
The start-up effects I am referring to are the effect of
backlash, the angle between stator and rotor, in-rush
current in the stator inductors, etc. on start-up.  Also
are the transforms you refer to  the physical --> abc -->
dq0 transforms? Also any insights into how much effort
should go into modeling the non-idealities of the stator
inductors and the air gap flux? For example, would you
expect the the stator inductor to saturate during
start-up? Does the air gap flux saturate during start-up?


                                                      Best Regards,

                                                         Sheldon