MC-D2 · Armature reaction & synchronous reactance

Armature Reaction and Synchronous Reactance

When load current flows, the armature also makes flux and disturbs the field flux. See how that effect changes sign with the power factor, and learn how to bundle all of it into a single 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 the effect depends on the phase of the current, that is, on the power factor. Before moving the power-factor-angle slider from lagging to leading to see how the phasors and the terminal voltage change, choose first whether armature reaction under a lagging load strengthens the flux or weakens it.

Power-factor angle φ (lag +, lead −)φ = 40°

The slider changes the power-factor angle continuously. Gold = V, blue = jIXs, green = E, and the orange arrow shows the direction of the armature current I. The figure keeps the sizes of E and of the current fixed and turns only the phase.

Terminal voltage and voltage regulation

V/E = 0.75 · ε = 33%

A lagging load does not strengthen the flux. Strengthening (magnetizing) happens with a leading (capacitive) load, when the terminal voltage actually rises; lagging is the opposite.

Lagging load — the reaction is?

Misaligned

Load current disturbs the flux

At no load only the field flux is present, so the terminal voltage equals the induced emf E. When load current flows, the three-phase armature winding also makes a rotating field, and this armature flux turns at the same speed as the field flux and merges with it. This 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.

Observeno load: V = E

At no load the terminal voltage equals the induced emf.

The power factor sets the sign of the reaction

With a purely resistive load (power factor 1) the armature current is nearly in phase with the induced emf, so the armature flux is at right angles in space to the field flux. It only distorts the flux sideways and leaves its size almost unchanged, which is called cross-magnetization. With a lagging (inductive) load the current falls behind, by 90° for a purely inductive load, and the armature flux opposes the field flux head-on and weakens it (demagnetizing). The terminal voltage drops by as much as the flux shrinks. With a leading (capacitive) load it is the other way round: the armature flux helps the field flux and strengthens it (magnetizing), so the terminal voltage rises. The same generator can see its terminal voltage fall or rise depending on the power factor of the load.

ChooseXs = Xreaction + ?

Armature-reaction reactance plus leakage reactance is the synchronous reactance.

Bundle every effect into the synchronous reactance

The flux change caused by armature reaction shows up, in the end, as a voltage proportional to the armature current. A voltage proportional to the current and leading it by 90° looks exactly like the voltage drop of a reactance, so this armature-reaction reactance is added to the winding's own leakage reactance and bundled into a synchronous reactance Xs. The per-phase equivalent circuit then becomes simply E = V + I(Ra + jXs), and since the armature resistance Ra is usually much smaller than the synchronous reactance, it is often neglected and the circuit is written E = V + jIXs. The voltage regulation is defined as (E - V)/V; it is large for a lagging load and can become negative for a leading load. The indicator in the figure uses the same formula, so moving the power-factor angle toward leading drives the regulation negative.

Fill inE = V + I ?

Neglecting armature resistance, E is V plus jIXs.

On your ownε = (E - V) / ?

Voltage regulation is the difference between induced emf and terminal voltage divided by the terminal voltage.

Back to the first screen

Under a lagging load armature reaction was demagnetizing, and the terminal voltage fell. The armature flux made by the load current combines with the field flux: under a lagging load it opposes and weakens it head-on, under a leading load it helps and strengthens it, and under a resistive load it only distorts it sideways, so it is the power factor that sets the sign of the reaction. Because this flux change appears in the end as a voltage proportional to the current and 90° ahead of it, it is bundled with the leakage into a synchronous reactance Xs, giving E = V + jIXs. This one equation linking the no-load E and the loaded V explains the voltage regulation of the synchronous generator and carries through to the next unit's synchronous motor and power-factor control.

Armature reaction: the armature flux of the load current combines with the field flux, and the power factor sets its sign. Lagging = demagnetizing (V↓), leading = magnetizing (V↑), resistive = cross-magnetizing. Bundling this reaction with the leakage into a synchronous reactance Xs gives the per-phase equivalent E = V + jIXs (Ra neglected), and the voltage regulation is (E - V)/V.

Once you hold this bundle

With a single synchronous reactance the behavior under load is summed up as E = V + jIXs, so the same machine can now be run as a motor. In the motor, the load angle (the phase difference between E and V) sets the torque, and changing the field excitation moves the power factor of the armature current from lagging to leading. That makes the synchronous motor a tool that produces torque and adjusts the power factor at the same time. The next unit (MC-D3) handles torque and power factor together through the load angle and the excitation.