The Synchronous Motor: Load Angle and Power-Factor Control

Over-excite the field and the power factor goes…

Once the load (the active power at the shaft) is set, the in-phase part of the armature current is fixed. But changing the internal EMF E with the field excitation changes the reactive part. Push the excitation slider and watch in the phasors whether the current I lags or leads the terminal voltage V. As you raise the excitation (over-excite), where does the power factor go?

The rotor is locked to the rotating field

In a synchronous motor the stator’s rotating field and the DC-excited rotor (a magnet) are magnetically locked and turn together at synchronous speed. Unlike the induction machine there is no slip. Under load the rotor falls back behind the field by the load angle δ, but the speed is unchanged. Torque is set by this angle as T ∝ (V E / Xs) sin δ. More load means a larger δ and more torque, but past δ = 90° the magnetic lock breaks and synchronism is lost (pulling out). So a synchronous motor cannot start by itself and needs a separate starting means.

Excitation buys and sells reactive power

Once the load is set, the active power the motor absorbs is set, and it corresponds to the part of the armature current in phase with the terminal voltage. This in-phase part is unchanged by excitation. But changing the internal EMF E with the field changes the reactive part. Under-excited (small E) the motor draws a lagging current and absorbs reactive power; over-excited (large E) it pushes a leading current and supplies reactive power. At the one excitation where the reactive part is zero, the power factor is unity and the armature current is least. Active power is held by the load angle, reactive power by the excitation, separately.

The synchronous condenser fixes power factor

The synchronous condenser is exactly this property put to use. A synchronous motor running with almost no shaft load, over-excited, supplies leading reactive power to the grid and improves the power factor — it acts like a giant capacitor. Run under-excited instead, it absorbs lagging reactive power and holds down the over-voltage that long transmission lines raise at light load. An ordinary loaded motor over-excited does the same, so in a factory a synchronous motor becomes a two-birds machine: it delivers power while improving the whole plant’s power factor.

Back to the first screen

Raising the excitation moved the power factor to leading. The active power set by the load was fixed in the in-phase part of the armature current, so the torque did not change, but the field excitation changed the magnitude of the internal EMF E and moved the reactive part of the current. Under-excited it absorbs reactive power lagging, over-excited it supplies it leading, and just right gives unity power factor with least armature current. This split — torque held by the load angle, power factor by the excitation — is what makes the synchronous motor special. Run over-excited at no load, it becomes a synchronous condenser that fixes power factor. The E = V + jIXs seen in the generator returns in the motor as the handle that grips torque and power factor at once.

Drawing the fact that excitation moves the power factor as one picture gives a V-shaped curve of armature current (vertical) against field current (horizontal). The valley is unity power factor, the left side under-excited (lagging), the right over-excited (leading). The whole curve rises with more load. The next unit quantifies the power-factor control with this V-curve and looks at how far the load angle can hold — the stability, the pull-out limit (MC-D4).