INDUCTION MOTOR

81

As this voltage may have any phase relation with regards to
the current, £1, we can put:

where:
and:

2 = (Pi

P =

tan w =

P*

(3)
(4)

(5)

is the angle of brush shift of the commutating machine.

(Pi + jp%) is of the nature and dimension of an impedance,
and we thus can put:

= Pi +jp*

(6)

as the effective impedance representing the commutating machine.
At the speed (1 — s),
the commutating machine is represented by -the effective
impedance:
.(1 - «) Z° = (1 - *) Pl + j (1 - s) ps. (7)
It must be understood, however, that in the effective impedance
of the commutating machine,
Z° = Pl + jp2,
Pi as well as p% may be negative as well as positive.
That is, the energy component of the effective impedance, or
the effective resistance, pi, of the commutating machine, may be
negative, representing power supply. This simply means, that
the commutator brushes are set so as to make the commutating
machine an electric generator, while it is a motor, if pi is positive.
If pi = 0, the commutating machine is a producer of wattless
or reactive power, inductive for positive, anti-inductive for
negative, ^2.
The calculation of an induction motor concatenated with a
commutating machine thus becomes identical with that of the
straight induction motor with short-circuited secondary, except
that in place of the secondary inductive impedance of the induc-
tion motor is substituted the total impedance of the secondary
circuit, consisting of:
1. The secondary self-inductive impedance of the induction
machine.
6