320

ELECTRICAL APPARATUS

III

Without losing in generality of the problem, we can, therefore,
assume the stator e.m.fs. in phase with the rotor e.m.fs., and the
polyphase shunt motor can thus be represented diagrammatically
by Fig. 152.

182. Let, in the polyphase shunt motor, shown two-phase in
diagram, Fig. 152:

EQ and — jEQj I0 and —jlo, Z0 = impressed e.m.fs., currents
and self-inductive impedance respectively of the stator circuits,

cEQ and —jcE0} Ii and —j/i, Zi = impressed e.m.fs., currents
and self-inductive impedance respectively of the rotor circuits,
reduced to the stator circuits by the ratio of effective turns, c,

Z = mutual-inductive impedance,

S = speed; hence s = 1 — S = slip,

0 = position angle between stator and rotor circuits, or
"brush angle."

It is then:
Stator:

Rotor:

c#o= -

+ Z

Substituting:

it is:

and:

Herefrom follows:

+ Z (/o - Ji cos 0 - ,?/! sin 19). (72)

•Jo cos 0 + jh sin 0) -
jSZ ( — jli + Jo sin 0 + jlo cos 0). (73)

Jo =

for c = o, this gives: •

ff 5
+
+
= cos 6 — j sin 6, = cos 9 + j sin 5,
a-5 = 1,
Z (Jo - 8/0, Z (/! - cr/o) + JSZ O'/i - j<r/o) SZ (/i - <r/o).
(s + 5c) Z + Z,
(74)
(75) (76) (77)
(78) (7G\

^aZZo + ZZi + ZoZi
r, (ffS + C) Z -f- C-Zi
V. n ... .. •. ---- ............ — 1

sZ

+ ZZi +