Two-reaction theory of synchronous machines with any balanced terminal impedance

R.H. PARK^{1, 2, 3} has presented a general analysis of salient-pole synchronous machines^∗ in terms of direct, quadrature, and zero axis quantities. This analysis is very well adapted to the case of a machine with balanced series inductance and resistance in the armature circuit, but requires modification for any other terminal impedance. S. B. Crary⁴ has recently extended the method of Park to include the effects of balanced armature circuit capacitance. In the present paper the same method of analysis is further extended to include the effects of any balanced impedance network connected to the armature terminals. Every concept (impedance operators, per-unit quantities, d and q axis quantities, etc.) of the previous synchronous machine theory is preserved unchanged in this extended theory, and every problem solvable by the previous theory is now susceptible to an exactly similar solution in the extended case. Such problems are, e.g.: 3-phase short circuit, sudden application or change of load, self-excitation, asynchronous operation, hunting, pulling into step, any prescribed change of field or armature voltage, torque under any of the conditions given above.