Reactances of synchronous machines

The reactances of synchronous machines comprise a set of characteristic constants used in the theory of synchronous machines.

[1] Technically, these constants are specified in units of the electrical reactance (ohms), although they are typically expressed in the per-unit system and thus dimensionless.

Since for practically all (except for the tiniest) machines the resistance of the coils is negligibly small in comparison to the reactance, the latter can be used instead of (complex) electrical impedance, simplifying the calculations.

[2] The air gap of the machines with a salient pole rotor is quite different along the pole axis (so called direct axis) and in the orthogonal direction (so called quadrature axis).

Andre Blondel in 1899 proposed in his paper "Empirical Theory of Synchronous Generators" the two reactions theory that divided the armature magnetomotive force (MMF) into two components: the direct axis component and the quadrature axis component.

[3] The relative strengths of these two components depend on the design of the machine and the operating conditions.

In machines with a cylindrical rotor the air gap is uniform, the reactances along the d and q axes are equal,[4] and d/q indices are frequently dropped.

The flux linkages of the generator vary with its state.

Usually applied for transients after a short circuit current.

) states are cheracterized by significantly smaller reactances.

Due to the presence of air gap, the role of the leakage flux is more important in a synchronous machine in comparison to a transformer.

[7] The synchronous reactances are exhibited by the armature in the steady-state operation of the machine.

[8] The three-phase system is viewed as a superposition of two: the direct one, where the maximum of the phase current is reached when the pole is oriented towards the winding and the quadrature one, that is 90° offset.

[9] The per-phase reactance can be determined in a mental experiment where the rotor poles are perfectly aligned with a specific angle of the phase field in the armature (0° for

In this case, the reactance X will be related with the flux linkage

[10] The conditions for this mental experiment are hard to recreate in practice, but: Therefore, the direct synchronous reactance can be determined as a ratio of the voltage in open condition

This models the machine by three components, each with a positive sequence reactance