REGULATING POLE CONVERTERS 447

^(l+O'a + PQ'MB'r.

7T2 m2

1 A

-- 2 (1 + 0 (1 + Pz) cos ra sin (ra + r&) tan 0i. (21)

T is a minimum for the value, 0i, of the phase displacement
given by :

-_

d tan 0i

and this gives, differentiated:

m* sin

7z ; — X~T^ — ; \

(1 +t} (1 + pi) COSTa

Equation (22) gives the phase angle, 02, for which, at given
ra, r6, t and 2?z, the armature heating becomes a minimum.

Neglecting the losses, pi, if the brushes are not shifted, T& = 0,
and no third harmonic exists, t = 0 :

tan 0'2 = m2 tanra,

where m2 = 0.544 for a three-phase, 0.912 for a six-phase
converter.

For a six-phase converter it thus is approximately 0'2 = ra,
that is, the heating of the armature is a minimum if the alter-
nating current lags by the same angle (or nearly the same angle)
as the magnetic flux is shifted for voltage regulation.

From equation (22) it follows that energy losses in the con-
verter reduce the lag, 02, required for minimum heating; brush
shift increases the required lag; a third harmonic, t, decreases
the required lag if additional, and increases it if subtractive.

Substituting (22) into (21) gives the minimum armature heat-
ing of the converter, which can be produced by choosing the
proper phase angle, 82, for the alternating current. It is then,
after some transpositions:

COS ra COS (ra + r&) — m2 sin2 (TO, + r&)

d

The terni To contains the constants £, pi, ra, n only in the
square under the bracket and thus becomes a minimum if this