The basic operation of all these generator types can be
explained using two simple rules, the first for magnetic circuits and the
second for the voltage induced in a conductor when subjected to a varying
magnetic field.
The means of producing a magnetic field using a current in
an electric circuit have shown that the flux Φ in a magnetic circuit which has
a reluctance Rm is the result of a magneto-motive force (mmf ) Fm, which itself
is the result of a current I flowing in a coil of N turns.
Φ = Fm/Rm and Fm = IN
The product of the rotor or field current I and the coil
turns N results in mmf Fm as in eqn 5.2, and this acts on the reluctance of the
magnetic circuit to produce a magnetic flux, the path of which is shown by the
broken lines in Fig. 5.4(b).
As the rotor turns, the flux pattern created by the mmf Fm
turns with it; this is illustrated by the second plot of magnetic flux in Fig.
5.4(b). When a magnetic flux Φ passes through a magnetic circuit with a cross
section A, the resulting flux density B is given by B = Φ/A Figure 5.4(a) also
shows a stator with a single coil with an axial length l.
As the rotor turns, its magnetic flux crosses this stator
coil with a velocity v, an electromotive force (emf ) V will be generated,
where V = Bvl (5.4)
The direction of the voltage is given by Fleming’s
right-hand rule, as shown in Fig. 2.6. Figure 5.4(b) shows that as the magnetic
field rotates, the flux density at the stator coil changes. When the pole face
is next to the coil, the air gap flux density B is at its highest, and B falls
to zero when the pole is 90° away from the coil.
The induced emf or voltage V therefore varies with time
(Fig. 5.5) in the same pattern as the flux density varies around the rotor
periphery. The waveform is repeated for each revolution of the rotor; if the
rotor speed is 3000 rpm (or 50 rev/s) then the voltage will pass through 50
cycles/second (or 50 Hz).
This is the way in which the frequency of the electricity
supply from the generator is established. The case shown in Fig. 5.4 is a 2-pole
rotor, but if a 4-pole rotor were run at 1500 rpm, although the speed is lower,
the number of voltage alternations within a revolution is doubled, and a
frequency of 50 Hz would also result.
The general rule relating the synchronous speed ns (rpm),
number of poles p and the generated frequency f (Hz) is given by f = nsp/120
The simple voltage output shown in Fig. 5.5 could be delivered to the point of
use (the ‘load’) with a pair of wires as a single-phase supply.
If more coils are added to the stator as shown in Fig.
5.4(a) and if these are equally spaced, then a three-phase output as shown in
Fig. 5.6 can be generated. The three phases are conventionally labelled ‘U’,
‘V’ and ‘W’. The positive voltage peaks occur equally spaced, one-third of a cycle
apart from each other.
The three coils either supply three separate loads, as shown
in Fig. 5.7(a) for three electric heating elements, or more usually they are
arranged in either ‘star’ or ‘delta’ arrangement in a conventional three-phase
circuit (Fig. 5.7(b)).
In a practical generator the stator windings are embedded in
slots, the induced voltage remaining the same as if the winding is in the gap
as shown in Fig. 5.4(b). Also, in a practical machine there will be more than
the six slots shown in Fig. 5.6(a). This is arranged by splitting the simple
coils shown into several subcoils which occupy separate slots, each phase still
being connected together to form a continuous winding. Figures 5.1 and 5.2 show
the resulting complexity in a complete stator winding.
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