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This paper describes a simplified one-phase equivalent circuit model of three-phase salient pole synchronous machines and synchronous reluctance machines. The model represents the pole saliency as a susceptance, with a magnitude based on the pole saliency and a phase angle based on twice the load angle. The reluctance torque itself is then modeled equivalent to a conductance. The model is made as an extension to Norton equivalents, where the internal inductance is connected as a shunt. This approach shares similarities to the magnetization shunt branch in circuit models of transformers and induction motors. The model is derived using the rotating dq-frame, using Park transform and two-reaction theory. The model is then rewritten to better fit one-phase equivalent circuit models, with the terminal voltage as the angular reference. The resulting two-pole model can then more easily be combined with basic circuit theory, thereby synthesizing dq-theory and phasor circuit models.
Mörée et al. (Wed,) studied this question.