Environmental Engineering Reference
In-Depth Information
v
dc in
N
Axis of
rotation
0
t
S
ac out
(a)
(b)
Figure 4.1 A two - pole synchronous generator. (Reproduced from Reference [1] with permission of
John Wiley & Sons, Inc.)
rotor built with permanent magnets. There are both advantages and disadvantages to each
type of excitation which will be explored later.
The fl ux density produced by the rotor in Figure 4.1(a) is maximum positive upwards along
the pole axis, zero at 90 ° to the pole axis and maximum negative at 180 °. Equation (4.1)
indicates that a variable voltage with polarity reversals is generated when the fi eld winding
rotates at constant angular velocity because the magnetic fi eld cutting each conductor increases
to a maximum, decreases and successively reverses in each revolution. By proper spatial
distribution of the stator winding turns and shaping of the pole faces, the generated voltage
across the stator terminals in Figure 4.1(a) can be made to approach the sinusoid waveform
shown in Figure 4.1(b). It should be evident that a full rotation of the rotor will result in a
full complete cycle of the sinusoidal waveform. Hence the frequency of the generated voltage
in Hz (cycles per second) is identical to the angular velocity of the rotor in revolutions per
second.
Appendix A explains that three-phase AC systems are universally used for the generation,
transmission and utilization of electrical energy. One of the reasons is that synchronous gen-
erators are particularly well suited for the generation of three-phase voltages. When wound
for three phases, alternators make optimal use of the iron that carries the magnetic fl ux and
of copper that carries the electric current. Figure 4.2(a) shows three separate one turn wind-
ings, where a, b and c indicate the beginnings and a
the ends of these windings.
The winding axes are shifted in space with respect to each other by 120 °. As a consequence
the voltages generated by the rotating fi eld are also shifted in the time domain by one third
of a period, thus forming the three-phase system of AC supply shown in Figure 4.2(b).
A more effective arrangement for superior power output from a three-phase stator winding
is shown in Figure 4.3. Here the winding is embedded and distributed in slots in an iron cyl-
inder. The magnetic fl ux
, b
and c
and therefore the fl ux density B generated by the rotating elec-
tromagnet is approximately proportional to the magnetomotive force (mmf) F (ampere turns)
given by
φ
F
=
NI f
(4.2)
where N is the number of turns of the fi eld winding (shown as having one turn in the fi gure)
and I f is the fi eld or excitation current. In a practical machine the air gap between the rotor
pole faces and the internal surface of the cylinder is made small, and the cylinder itself is
made of a ferromagnetic material so that minimum resistance is offered to the fl ow of mag-
netic fl ux. A large radial magnetic fl ux can therefore be produced from a moderate I f .
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