MC-D1 · Synchronous generator principle

The Synchronous Generator and Its Induced EMF

A synchronous generator makes electricity by spinning a magnet. Turn a DC-excited rotor and see for yourself, by changing the rotating speed, what the frequency of the electricity it produces is tied to.

If you make the rotor speed 2 times higher, the frequency…

The rotor is an N · S pole pair set up by DC excitation. As this magnet turns, the flux seen by each stator phase varies sinusoidally and a three-phase emf is induced. In one revolution the emf oscillates as many times as there are pole pairs, so raising the speed slider makes the waveforms on the right run faster. Pick first what happens to the frequency when the speed becomes 2 times higher, then check with the slider.

Rotor speed NN = 1800 rpm

The slider changes the rotating speed continuously. The rotor on the left is drawn with one pole pair (N · S) turning at the electrical angle, the right shows the emf of the three phases a · b · c, and the indicator's calculation is for a 4-pole machine.

Frequency locked to speed: f = PN/120

f = 4×1800/120 = 60 Hz

Raising the speed cannot halve the frequency. The frequency is directly proportional to the rotating speed: the faster the rotor turns, the more often the stator flux reverses and the faster the emf oscillates.

N made 2× — f is?

Misaligned

The opposite layout to the induction machine

In the induction machine the stator built the rotating field and the rotor chased it. The synchronous generator is the reverse: the rotor makes the flux itself. Direct current in the rotor winding (the field) sets up N · S poles, and when a prime mover such as a turbine turns this magnet, the three-phase winding of the stator (the armature) links the rotating flux and an emf is induced. Large machines turn the small field that makes the flux, the revolving-field type, so that the large armature current can be taken straight from the stationary stator rather than from a moving part. The direct current the field needs is fed in through slip rings or supplied by a brushless exciter mounted on the rotor.

Observef = PN120

The frequency is the product of pole number and speed divided by 120.

Frequency locked to rotor speed

In a 2-pole machine the flux reverses once per revolution of the rotor and the emf traces one cycle; in a P-pole machine one revolution gives P/2 cycles. So the frequency is f = PN/120 [Hz, N in rpm], and making 60 Hz takes 3600 rpm with 2 poles, 1800 with 4 poles and 1200 with 6 poles. The generator's rotating speed is the grid frequency, so to hold the frequency the speed of the prime mover is held precisely by a governor. The same formula is why slow-turning machines such as hydro generators have dozens of poles, and because speed and frequency are bound together beyond separating, this machine is called a synchronous machine.

ChooseE = 4.44 f N ?

The induced emf is proportional to the product of frequency, turns and flux.

Fill inE = 4.44 f N Φ ?

The winding factor accounts for the emf lost to distributed and short-pitched windings.

The size of the EMF and excitation

The induced emf of one 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 1 that accounts for the coils being spread over several slots (distributed winding) and made a little narrower than the pole pitch (short-pitched winding), so that the emfs of the individual coils are out of phase and their sum is slightly less than the arithmetic sum. Short pitching gives up a little emf this way but cuts harmonics and brings the waveform closer to a sine. The flux Φ is set by the DC excitation current in the field, so raising the excitation raises the flux and the emf nearly in proportion until the core saturates; if speed sets the frequency, excitation sets the size of the voltage.

On your ownΦ ∝ ?

The flux is adjusted with the DC excitation current of the field.

Back to the first screen

Making the speed 2 times higher made the frequency 2 times higher too. Each revolution of the DC-excited rotor reverses the stator flux as many times as there are pole pairs and produces that many emf cycles, so the frequency is tied one-to-one to the rotating speed by f = PN/120, and holding the grid frequency is the same job as holding the generator's rotating speed. The size of the emf is E = 4.44 f N Φ kw: on top of the frequency set by the speed, the field excitation current sets it separately through the flux Φ. Where the induction machine let its speed fall away from synchronous speed by the slip, the synchronous machine binds speed and frequency as one.

Synchronous generator: turning a DC-excited rotor (a magnet) at synchronous speed induces an emf in the three-phase stator winding, and its frequency is tied to the speed, f = PN/120. The induced emf per phase is E = 4.44 f N Φ kw (kw = winding factor); the 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 generator with no load. When load current flows in the armature, the flux it creates combines with the field flux, so the armature reaction met in the DC machine appears in the synchronous machine as well. In the synchronous machine, though, the effect weakens or strengthens the field flux depending on the power factor, and it is handled by bundling it into a single synchronous reactance. The next unit (MC-D2) works out, with armature reaction and synchronous reactance, how the terminal voltage changes under load.