Armature Reaction and Synchronous Reactance

Under a lagging (inductive) load, the armature reaction is…

At no load the terminal voltage equals the induced EMF E. Under load, the flux made by the armature current I combines with the field flux, and that effect depends on the current’s phase (the power factor). Move the power-factor-angle slider from lagging to leading and watch the phasors and the terminal voltage. Under a lagging load, does the armature reaction grow the flux or trim it?

Load current disturbs the flux

At no load only the field flux is present and the terminal voltage equals the induced EMF E. Under load the armature three-phase winding also makes a rotating field, and this armature flux turns at the same speed as the field flux and combines with it. The resultant flux is the actual air-gap flux and sets the terminal voltage. So under load the terminal voltage differs from its no-load value. How much, and in which direction, depends on the phase of the armature current.

The power factor sets the sign of the reaction

Under a resistive load (unity power factor) the armature current is in phase with the induced EMF, so the armature flux is spatially at right angles to the field flux. It only distorts it sideways, leaving the magnitude nearly unchanged (cross-magnetizing). Under a lagging (inductive) load the current lags another 90°, so the armature flux directly opposes and trims the field flux (demagnetizing); the flux falls and the terminal voltage drops. Under a leading (capacitive) load the opposite holds: the armature flux aids the field flux (magnetizing); the flux grows and the terminal voltage rises. The same generator can have its terminal voltage drop or rise depending on the load’s power factor.

Bundle every effect into the synchronous reactance

The flux change of armature reaction ultimately shows up as a voltage effect proportional to the armature current. Being a voltage proportional to current and leading it by 90°, it is exactly the voltage drop a reactance makes. So this reaction reactance is added to the winding’s own leakage reactance into one synchronous reactance Xs. The per-phase equivalent circuit then tidies to E = V + I(Ra + jXs). The armature resistance Ra is usually small and often dropped, giving E = V + jIXs. The voltage regulation is (E - V)/V, large under a lagging load and sometimes negative under a leading one.

Back to the first screen

Under a lagging load the armature reaction was demagnetizing and the terminal voltage dropped. The armature flux made by the load current combines with the field flux, but opposes and trims it when lagging, aids and grows it when leading, and only distorts it sideways when resistive. The power factor sets the sign of the reaction. Since this flux change is ultimately a voltage proportional to current and leading by 90°, it bundles with the leakage into one synchronous reactance Xs, giving E = V + jIXs. This single equation linking the no-load E and the loaded V upholds the generator’s voltage regulation and, in the next unit, the synchronous motor and its power-factor control.

With load behaviour tidied into E = V + jIXs by a single synchronous reactance, the same machine can now run as a motor. In a motor the load angle (the phase between E and V) sets the torque, and changing the field excitation shifts the armature current’s power factor from lagging to leading. So a synchronous motor becomes a tool that makes torque and adjusts power factor at once. The next unit handles torque and power factor together through load angle and excitation (MC-D3).