if!

[ I!

?

t

4 '-,

M

< •'

i I i

1 fj }J

i

i rf }«

Hi

M.li

*!J
j '*•

/ {/

446

ELECTRICAL APPARATUS

and equations (19) and (20) assume the form:
Three-phase:

1.185

Six-phase:

•p __

•p

COS2 61

0.889
cos2 0i

- 0.621.

- 0.621.

The equation (18) is the most general equation of the relative
heating of the synchronous converter, including phase displace-
ment, 0i, losses, pi, shift of brushes, n, shift of the resultant mag-
netic flux, TC) and the third harmonic, t.

While in a converter of standard or normal ratio the armature
heating is a minimum for unity power-factor, this is not in gen-
eral the case, but the heating may be considerably less at same
lagging current, more at leading current, than at unity power-
factor, and inversely.

245. It is interesting therefore to determine under which con-
ditions of phase displacement the armature heating is a minimum
so as to use these conditions as far as possible and avoid con-
ditions differing very greatly therefrom, as in the latter case
the armature heating may become excessive.

Substituting for k and 0o from equations (8) and (10) into
equation (18) gives:

T = 1 +

8(1

n2 sin2 - cos2 0j
n

16 (* +00-+ PP. COS ra COS (0! -Tg - Tb)

Substituting:

.

7T2 COS 01

- sin - = m, (20)
TT n

(19)

which is a constant of the converter type, and is for a three-
phase converter, ms = 0.744; for a six-phase converter, w6 =
0.955; and rearranging, gives:

T^ - 1 _1_ 8 (1 + Q2 (1 + ?>02 COS2 ra

1 " A + 7T2 ^

-----a (1 + 0 (1 + ?0 COS ra COS (ra -f r&)

1 !!J