80 ELECTRICAL APPARATUS
the induction machine, the phase of the synchronous machine is
fa ,i i fixed in space, by the synchronous-motor poles, thus has a fixed
1! [ relation with regards to the induction-motor primary system.
! I * As, however, the induction-motor secondary has no fixed position
fl ' relation with regards to the primary, but can have any position
{-,<; *' slip, the synchronous-motor voltage has no fixed position with
S'j • , regards to the induction-motor secondary voltage and current,
<t! l| thus can assume any position, depending on the relation in the
$ secondary circuit. Thus if we assume that the synchronous-
\\ \ motor field were shifted in space by a position degrees (electrical):
\\ < this would shift the phase of the synchronous-motor voltage by
jtlj a degrees, and the induction-motor secondary would slip in posi-
jj1 ' tion by the same angle, thus keep the same phase relation with
^ ' regards to the synchronous-motor voltage. In the couple with
^ , I a commutating machine as secondary motor, however, the posi-
Y i , tion of the brushes fixes the relation between commutating-
j * machine voltage and secondary current, and thereby imposes a
definite phase relation in the secondary circuit, irrespective of
)| the relations between secondary and primary, and no change of
,/< j relative position between primary and secondary can change this
1 phase relation of the commutating machine.
Jg , . Thus the commutating machine in the secondary of the induc-
?J tion machine permits a far greater variation of conditions of
,j | operation, and thereby gives a far greater variety of speed and
J | load curves of such concatenated couple, than is given by the
!i use of a synchronous motor in the induction-motor secondary.
14 53. Assuming the polyphase low-frequency commutating
/< machine is series-excited, that is, the field coils (and compensat-
I ing coils, where used) in series with the armature. Assuming
I also that magnetic saturation is not reached within the range of
its use.
The induced voltage of the commutating machine then is
proportional to the secondary current and to the speed.
Thus: • €2 = pz'i (1)
is the commutating-machine voltage at full synchronous speed,
where ii is the secondary current and p a constant depending
on the design.
. At the slip, 8, and thus the speed (1 — 5), the commutating
machine voltage thus is:
(I1- 5)62 = (1 - a) PU. (2)