518 ELECTROMECHANICS
In fact, with very few exceptions, three-phase synchronous machines are most commonly
used for power generation. In general, three-phase ac power systems, including power generation,
transmission, and usage, have grown most popular because of their economic advantages. An
elementary three-phase, two-pole synchronous machine with one coil per phase (chosen for
simplicity) is shown in Figure 12.2.3(a). The coils are displaced by 120 electrical degrees from
each other in space so that the three-phase voltages of positive phase sequencea–b–c,displaced
by 120 electrical degrees from each other in time, could be produced. Figure 12.2.3(b) shows
an elementary three-phase, four-pole synchronous machine with one slot per pole per phase. It
has 12 coil sides or six coils in all. Two coils belong to each phase, which may be connected in
series in either wye or delta, as shown in Figures 12.2.3(c) and (d). Equation (12.2.12) can be
applied to give the rms voltage per phase whenNis treated as the total series turns per phase.
The coils may also be connected in parallel to increase the current rating of the machine. In
actual ac machine windings, instead of concentrated full-pitch windings, distributed fractional-
pitch armature windings are commonly used to make better use of iron and copper and to make
waveforms of the generated voltage (in time) and the armature mmf (in space) as nearly sinusoidal
as possible. That is to say, the armature coils of each phase are distributed in a number of slots, and
the coil span may be shorter than a full pitch. In such cases, Equation (12.2.12) is modified to be
Erms= 4. 44 kWfNphφV/phase (12.2.13)
wherekWis a winding factor (less than unity, usually about 0.85 to 0.95), andNphis the number
of series turns per phase.
Special mechanical arrangements must be provided when making electrical connections to
the rotating member. Such connections are usually made through carbon brushes bearing on either
aslip ringor acommutator,mounted on—but insulated from—the rotor shaft and rotating with
the rotor. A slip ring is a continuous ring, usually made of brass, to which only one electrical
connection is made. For example, two slip rings are used to supply direct current to the field
winding on the rotor of a synchronous machine. A commutator, on the other hand, is a mechanical
switch consisting of a cylinder formed of hard-drawn copper segments separated and insulated
from each other by mica.
In the conventionaldc machine(with a closed continuous commutator winding on its
armature), for example, full-wave rectification of the alternating voltage induced in individual
armature coils is achieved by means of a commutator, which makes a unidirectional voltage
available to the external circuit through the stationary carbon brushes held against the commutator
surface. The armature windings of dc machines are located on the rotor because of this necessity for
commutation and are of the closed continuous type, known aslapandwavewindings. The simplex
lap winding has as many parallel paths as there are poles, whereas the simplex wave winding
always has two parallel paths. The winding connected to the commutator, called thecommutator
winding,can be viewed as a pseudostationary winding because it produces a stationary flux when
carrying a direct current, as a stationary winding would. The direction of the flux axis is determined
by the position of the brushes. In a conventional dc machine, in fact, the flux axis corresponds
to the brush axis (the line joining the two brushes). The brushes are located so that commutation
(i.e., reversal of current in the commutated coil) occurs when the coil sides are in the neutral
zone, midway between the field poles. The axis of the armature mmf is then in the quadrature
axis, whereas the stator mmf acts in the field (or direct) axis. Figure 12.2.4 shows schematic
representations of a dc machine. The commutator is thus a device for changing the connections
between a rotating closed winding and an external circuit at the instants when the individual
coil-generated voltages reverse. In a dc machine, then, this arrangement enables a constant and
unidirectional output voltage. The armature mmf axis is fixed in space because of the switching