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You can divide the synchronous machines in 2 groups, based on the principle they employ to generate torque:
- interaction of 2 independent fields, one generated on stator and the other on the rotor: let's call this group "excited" synchronous machines;
- the torque is generated by an anisotropic rotor structure and the presence of a magnetic field generated by the stator: the latter field will tend to attract the anisotropic rotor in order to minimize the reluctance of the path of the magnetic field itself; let's call this group "reluctance" machines.

Then, of course, you can also mix the 2 things, by providing an anisotropic structure with some way (see down) to independently excite a rotor field.

Now, 2 additions to the above: in the 1st group the excitation of the rotor field can be provided by both a field winding fed with current through slip-rings and brushes (the traditional power plant alternator) and then will call it "electrically excited" synchronous; or, excitation can be provided by permanent magnets placed somewhere in the rotor structure (either on the outer surface or inside), and then we'll call it "PM synchronous" machine.

Second precaution: though the physical principle is the same, *synchronous* reluctance machines are quite different from *switched* reluctance ones. The latter, in fact, have a salient structure also on the stator, the coils being supplied (a phase at a time) with DC current, that produces a magnetic field fixed in space: once the minimal reluctance position is achieved, the rotor would continue stay there (neglecting little oscillations) unless current is moved to a different phase. In *synchronous* reluctance, instead, the stator structure is more conventional, almost isotropic, and a set of AC currents is supplied to all the coils: this generates a rotating magnetic field, hence your "preferred position" is not reached and the rotor continues spinning.

Induction machine is actually an Asynchronous machine in nature with windings (or bars as in the case of squirrel cage IMs) on both the stator and the rotor. In the case of Induction machine, the MMFs of the rotor and the stator must be in Asynchronization in order to produce what is many times referred to as Slip. Hence, to change the speed of the IM, one must change the Slip (Asynchronization between the rotor and stator MMFs) of the machine. For more mathematical explanation of the operation of the IM, please look at the T-equivalent circuit for steady-state operation of a symmetrical induction machine.

It is important to note that Induction machine is a class of an electrical machine. However, Synchronous machine is solely a behavioral definition (machine is rotating with synchronization with the MMF) and does not refer to a particular machine class; for instance 'permanent magnet synchronous machine' and 'wound rotor synchronous machine' are two very different machine classes, but they are still "behaviorally" synchronous machines.
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