MC-D1 · Synchronous generator principle

The Synchronous Generator and Its Induced EMF

A synchronous generator makes electricity by spinning a magnet. As the DC-excited rotor turns, see what the frequency of the electricity it makes is tied to, by varying the rotor speed.

If you double the rotor speed, the frequency…

The rotor is a steady N-S magnet made by DC excitation. As it spins, the flux each stator phase sees varies sinusoidally and a three-phase EMF is induced. In one revolution the EMF oscillates as many times as the pole pairs. Raise the speed slider and watch the waveform quicken. If you double the speed, what happens to the frequency?

Rotor speed NN = 1800 rpm

Slide for continuous speed. The rotor is the magnet, the right side is the three-phase EMF.

Frequency locked to speed: f = PN/120

f = 4×1800/120 = 60 Hz

The frequency cannot halve when you raise the speed. Frequency is directly proportional to rotor speed. The faster the rotor turns, the more often the stator flux reverses and the faster the EMF oscillates.

Double N — f is?

Misaligned

The opposite layout to the induction machine

In the induction machine the stator made the rotating field and the rotor chased it. The synchronous generator is the opposite: the rotor makes the flux itself. DC is fed into the rotor winding (the field) to set up a steady N-S magnet, and this magnet is turned by a prime mover such as a turbine. The stator (the armature) three-phase winding has its EMF induced by this rotating flux. Large machines use the rotating-field type, turning the small field that makes the flux, so the large armature current is taken from the stationary stator rather than a spinning part.

Observef = PN120

Frequency is the pole number times speed over 120.

Frequency locked to rotor speed

In one revolution a 2-pole machine flips the flux once and the EMF draws one cycle; a P-pole machine makes P/2 cycles per revolution. So the frequency is f = PN/120 [Hz, N in rpm]. To make 60 Hz a 2-pole must spin at 3600, a 4-pole at 1800, and a 6-pole at 1200 rpm. Because the generator’s speed is the grid frequency, holding the frequency steady requires a governor to hold the prime mover’s speed precisely. Speed and frequency are inseparably locked, which is why it is called synchronous.

ChooseE = 4.44 f N ?

The EMF is proportional to frequency, turns and flux.

Fill inE = 4.44 f N Φ ?

The winding factor corrects the EMF trimmed by distribution and short pitch.

The size of the EMF and excitation

The induced EMF per phase is E = 4.44 f N Φ kw. Here f is the frequency, N the series turns per phase, Φ the flux per pole, and kw the winding factor. The winding factor is a number less than one that corrects for the EMF coming out slightly below the arithmetic sum because the coils are spread over several slots (distribution) and made narrower than the pole pitch (short pitch). The flux Φ is set by the DC excitation current in the field, so raising the excitation raises the flux and the EMF. If speed sets the frequency, excitation sets the size of the voltage.

On your ownΦ ∝ ?

The flux is set by the DC field excitation current.

Back to the first screen

Doubling the speed doubled the frequency. Each revolution of the DC-excited rotor flips the stator flux as many times as the pole pairs and makes that many EMF cycles, so the frequency is locked one-to-one to speed as f = PN/120. Holding the grid frequency is therefore the same as holding the generator’s speed. Meanwhile the size of the EMF is E = 4.44 f N Φ kw: on top of the frequency that speed sets, the field excitation current sets the size of the voltage separately through the flux Φ. Where the induction machine let speed slip away, the synchronous machine binds speed and frequency into one body.

The synchronous generator: spinning a DC-excited rotor (a magnet) at synchronous speed induces an EMF in the stator three-phase winding, with its frequency locked to speed as f = PN/120. The EMF per phase is E = 4.44 f N Φ kw (kw = winding factor). Speed sets the frequency, and the field excitation current sets the size of the voltage through the flux Φ.

Once you hold this principle

So far this was a no-load generator. When load current flows in the armature, the flux it creates combines with the field flux, and the armature reaction seen in the induction machine appears here too. In a synchronous machine, though, that effect adds to or subtracts from the flux depending on the power factor, and it is bundled into a single synchronous reactance. The next unit sees how the terminal voltage changes under load through armature reaction and synchronous reactance (MC-D2).