INDUCTION MOTOR

61

Thus, the minimum possible value of the counter e.m.f., e,
is given by equating the square root to zero, as:

x
e = ~eo.

For a given value of the counter e.m.f., e, that is, constant
field excitation, it is, from (7):

o .

*2 - ~ ± - », -

(10)

or, if the synchronous impedance, x, is very large compared with
r, and thus, approximately:

z = x:
t, = f ± ^ - .-,«. (11)

The maximum value, which the energy current, ii, can have,
at a given counter e.m.f., e, is given by equating the square root
to zero, as:

*~ (12)

For: ii = 0, or at no-load, it is, by (11):

. __ ip + e
2 x

Equations (9) and (12) give two values of the currents i\
and 12, of which one is very large, corresponds to the upper or
unstable part of the synchronous motor-power characteristics
shown on page 325 of " Theory and Calculation of Alternating-
current Phenomena/7 5th edition.

43. Denoting, in equation (5):

# = e' - je", (13)

and again choosing $0 = e0, as the real axis, (5) becomes:

and the electric power input into the motor then is:

__ /rrr r it

0 = /#0> */

= 6oZ*i, (15)

the power output at the armature conductor is:

= e'ii + e"i3,