MC-D3 · Synchronous motor & power factor

The Synchronous Motor: Load Angle and Power-Factor Control

The synchronous motor is a rare machine whose torque and power factor can be held separately. With the load fixed, change only the field excitation and follow for yourself where the power factor of the armature current goes.

Over-excite the field and the power factor goes…

Once the load on the shaft, that is, the real power, is set, the in-phase part of the armature current is fixed. But changing the size of the internal emf E with the field excitation changes the reactive part of the current, and with it whether the current I lags or leads the terminal voltage V on the phasor diagram. Pick first where the power factor goes when the excitation is raised (overexcitation), then push the slider and check.

Field excitation |E||E| = 0.60

The slider changes only the excitation, continuously, with the load fixed. Gold = V, green = E, copper = I. The blue arrow is jIXs, and because the real power stays the same, the tip of I moves only along a vertical line and the tip of E only along a horizontal line.

Power factor and armature current

pf = 0.53 (lag) · |I| = 1.13

With overexcitation the current does not lag. Lagging belongs to underexcitation, when the excitation falls short: the motor then draws a lagging current from the grid and absorbs reactive power, and raising the excitation moves it the other way.

Over-excited — the power factor is?

Misaligned

The rotor is locked to the rotating field

In a synchronous motor the rotating field of the stator and the DC-excited rotor (a magnet) lock together magnetically and turn together at synchronous speed. Unlike the induction machine there is no slip, so when load is applied the rotor only falls behind the rotating field by the load angle δ and the speed stays the same. The torque is set by this load angle, T ∝ (V E / Xs) sin δ; as the load grows δ grows and the torque rises, but once δ passes 90° the magnetic lock breaks and synchronism is lost (pull-out). Also, a rotor at standstill cannot latch onto a field turning at synchronous speed, so the motor cannot start by itself; it starts like an induction machine on a damper winding fitted to the rotor, or with an inverter that raises the frequency from a low value.

ObserveT ∝ (VEXs) sin δ

Torque is proportional to the sine of the load angle.

Choosepull-out: δ = ?

Once the load angle passes 90°, synchronism is lost (pull-out).

Excitation buys and sells reactive power

Once the load is set, the real power the motor absorbs is set, and it corresponds to the part of the armature current in phase with the terminal voltage, so this part stays the same when the excitation changes. But changing the size of the internal emf E with the field excitation changes the reactive part of the current. Underexcited (E small), the motor draws a lagging current from the grid and absorbs reactive power; overexcited (E large), it sends a leading current and supplies reactive power. At the one point where the excitation is just right, the reactive part becomes 0, the power factor becomes 1, and the armature current is smallest. Real power is handled by the load angle, reactive power by the excitation.

Fill inover-exc → I: ?

Changing the excitation changes the reactive part of the current.

The synchronous condenser fixes power factor

The synchronous condenser is this property put to direct use. Running a synchronous motor with almost no load on its shaft overexcited supplies leading reactive power to the grid and corrects the power factor, so it acts like a huge capacitor. Run underexcited instead, it absorbs lagging reactive power and holds down the voltage rise that the capacitance of a long transmission line causes at light load (the Ferranti effect). Unlike a capacitor bank, it can move continuously between supplying and absorbing with the excitation alone. An ordinary loaded synchronous motor does the same when run overexcited, so in a factory it delivers mechanical power while also correcting the power factor of the whole plant.

On your ownno-load over-exc = ?

A synchronous motor run overexcited at no load is a synchronous condenser.

Back to the first screen

Raising the excitation moved the power factor to leading. The real power set by the load stayed fixed as the in-phase part of the armature current, so the torque did not change, but the field excitation changed the size of the internal emf E and moved the reactive part of the current. Underexcited, the motor absorbs reactive power with a lagging current; overexcited, it supplies it with a leading current; just right, the power factor is 1 and the armature current is smallest. This split, with torque held by the load angle and power factor by the excitation, is what makes the synchronous motor special, and running it overexcited at no load turns it straight into a synchronous condenser that corrects the power factor. The E = V + jIXs met in the generator, with the current direction reversed for a motor so that jIXs is subtracted, becomes a handle for torque and power factor at once.

Synchronous motor: the rotor locks onto the rotating field and turns at synchronous speed, and the torque is set by the load angle, T ∝ (VE/Xs)sinδ (pull-out if δ>90°). With the load (real power) fixed, the field excitation adjusts the power factor: underexcited = lagging (absorbs reactive power), overexcited = leading (supplies reactive power), and just right gives power factor 1 and minimum current. Overexcited operation at no load is a synchronous condenser.

Once you hold this control

Drawing on a single graph how excitation moves the power factor, with field current on the horizontal axis and armature current on the vertical, gives a V-shaped curve. The bottom of the V is power factor 1, the left side is underexcited (lagging), the right side overexcited (leading), and the whole curve rises as the load grows. The next unit (MC-D4) uses this V-curve to put numbers on power-factor control and also works out stability (the pull-out limit), how far the load angle can hold.