II

408

ELECTRICAL APPARATUS

Hence 62 is near zero for all except very low speeds.

For very low speeds, a is small, and #2 thus large and positive.

That is, the voltage, $2, impressed upon the compensating
circuit to get negligible commutation current, must be approxi-
mately in phase with e for all except low speeds. At low speeds,
it must lag, the more, the lower the speed. Its absolute value
is very large at low speeds, but decreases rapidly with increasing
speed, to very low values.

For instance, let, as before:

X4 = 0.304 - 0.248 j,
Co = 0.4,
b = 10;

it is:

hence:

tan (02 -f a) = 5.05,
02 -f <r = 79°;

= 79° _

02 = 0 for <r = 79°; hence, by (116), So = 2.02, or double syn-
chronism. Above this speed, 02 is leading, but very small, since
the maximum leading value, for infinite speed, S = °°, is given
by <r = 90°, as, 02 == —11°. Below the speed, So, 02 is positive,
or lagging;
for S = 1, it is cr = 68°, 02 = +11°, hence still approximately
in phase;
for S = 0.4, it is cr = 45°, 02 = 34°; hence E$ is still nearer in
phase than in quadrature to e.
The corresponding values of T = t' •+ I" are, from (112):
S = 2.02, 02 = 0, T = 0.197, t = 0.197,
5 = 1, 02 = +11°, T = 0.747 -f 0.140 j, t = 0.760,
S = 0.4, 02 = 34°, T = 3.00 -2.00 j, t = 8.61.
224. The introduction of a phase displacement between the
compensating voltage, j^2, and the total voltage, e, in general is
more complicated, and since for all but the lowest speeds the
required phase displacement, 02, is small, it is usually sufficient
to employ a compensating voltage, e%, in phase with e.
In this case, no value of t exists, which makes the commutation
current vanish entirely, except at the speed, S0.
The problem then is, to determine for any speed, S, that value