Synchronous machines - Steady-state modeling

Like all electrical machines, synchronous machines are reversible, and the transition from motor to generator mode is continuous. In this document, we adopt generator operation by convention, as motor operation can be obtained by simply reversing the electromotive force or armature current. Furthermore, the models presented here remain conventional, and all waveforms are assumed to be sinusoidal, except at the end of the text, where a more rigorous model is proposed. These models are potentially suitable for all synchronous machines, but are particularly well suited to heteropolar machines with rotating fields and distributed windings. We start with machines with constant air gap or "smooth poles", in unsaturated operation. Their modeling provides a useful first approach to understanding the specific properties and applications of synchronous machines in general. Magnetic saturation is then taken into account using the Potier method. Next, the two-axis modeling (Blondel method) of salient-pole machines is described. Finally, the application of the virtual work method provides a rigorous model capable of taking into account the main non-linearities.

Wherever necessary, two electrical representations are given: one corresponding to the case where the rotor position is known, suitable for autopilot operation (Fresnel representation in the d-q plane), and the other where the rotor position is unknown, suitable for open-loop operation (classical representation). In addition, torque expressions will be provided for the two types of electrical sources associated with the machine: voltage source and current-controlled source. These approaches make it possible to apply the proposed models to the various uses of steady-state synchronous machines, whether associated with an electrical network or a static converter.

This dossier follows on from the "Synchronous machines: general principles and structures" dossier in this treatise. . Readers may therefore wish to refer to it, particularly for certain definitions or preliminary calculations such as air-gap surface permeance or magnetomotive forces.