A New Interpretation of the Steady-State Two-Reaction Theory of a Salient-Pole Synchronous Machine

This work contributes two improvements to the well-established two-reaction theory of a salient-pole synchronous machine. Namely, a single circuit is proposed that explicitly accounts for the saliency in the machine. By defining new machine reactances and using a current-controlled voltage source, the proposed single circuit proposed provides an alternative to coupled $d$ - and $q$ -axis circuit models. The new reactances are also used in a revised phasor diagram to make apparent the internally developed power of a salient-pole synchronous machine that is similar to a round-rotor synchronous machine. The revised two-reaction theory is illustrated using the mathematical model of a three-phase salient-pole synchronous machine whose equations are derived using complex space vectors instead of traditional matrix transformations. A detailed derivation is presented and the resulting equations can directly be used to solve for the steady-state operating EMF and power angle from the terminal voltages and currents in the $abc$ coordinate system. The ease of their application is demonstrated using a numerical example of the steady-state circuit equations and the revised phasor diagrams.