CHAPTER III
CONCATENATION
Cascade or Tandem Control of Induction Motors
28. If of two induction motors the secondary of the first motor
is connected to the primary of the second motor, the second
machine operates as a motor with the voltage and frequency
impressed upon it by the secondary of the first machine. The
first machine acts as general alternating-current transformer
or frequency converter (see Chapter XII), changing a part of the
primary impressed power into secondary electrical power for
the supply of the second machine, and a part into mechanical
work.
The frequency of the secondary voltage of the first motor, and
thus the frequency impressed upon the second motor, is the fre-
quency of slip below synchronism, s. The frequency of the
secondary of the second motor is the difference between its im-
pressed frequency, s, and its speed. Thus, if both motors are
connected together mechanically, to turn at the same speed,
1 — Sj and have the same number of poles, the secondary fre-
quency of the second motor is 2 s — 1, hence equal to zero at
s = 0.5. That is, the second motor reaches its synchronism at
half speed. 'At this speed, its torque becomes zero, the power
component of its primary current, and thus the power com-
ponent of the secondary current of the first motor, and thus also
the torque of the first motor becomes zero. That is, a system of
two concatenated equal motors, with short-circuited secondary
of the second motor, approaches half synchronism at no-load,
in the same manner as a single induction motor approaches
synchronism. With increasing load, the slip below half syn-
chronism increases.
In reality, at half synchronism, s = 0.5, there is a slight torque
produced by the first motor, as the hysteresis energy current of
the second motor comes from the secondary of the first motor,
and therein, as energy current, produces a small torque.
More generally, any pair of induction motors connected in
concatenation divides the speed so that the sum of their two