V. Armature Reaction 93. The armature reaction of the polyphase converter is the resultant of the armature reactions of the machine as direct- current generator and as synchronous motor. If the com- mutator brushes are set at right angles to the field poles or without lead or lag, as is usually done in converters, the direct- current armature reaction consists in a polarization in quadra- ture behind the field magnetism. The armature reaction due to the power component of the alternating current in a synchro- nous motor consists of a polarization in quadrature ahead of the field magnetism, which is opposite to the armature reaction as direct-current generator. Let m = total number of turns on the bipolar armature or per pair of poles of an n-phase converter, / = direct current, then the number of turns in series between the brushes = -~, hence the total armature ampere-turns, or polarization, = -^— Since, how- 16 * 246 ELEMENTS OF ELECTRICAL ENGINEERING ever, these ampere-turns are not unidirectional, but distributed over the whole surface of the armature, their resultant is ml avg. cos and, since avg. cos T 2 ml we have F = — - = direct-current polarization of the converter 7T (or direct-current generator) armature. vn In an n-phase converter the number of turns per phase = n The current per phase, or current between two adjacent leads (ring current), is 7T n sin — n hence, the ampere-turn per phase, ml' \/2 ml n n sin - n These ampere-turns are distributed over - of the circumference of the armature, and their resultant is thus ml' and, since we have n avg. cos avg. cos n . TT = - sin -i . ;'» n irn = resultant polarization, in effective ampere-turns of one phase of the converter. The resultant m.m.f. of n equal m.m.fs. of effective value of FI, thus maximum value of FI \/2, acting under equal angles SYNCHRONOUS CONVERTERS 247 — , and displaced in phase from each other by - of a period, or 71 71 phase angle — , is found thus: = Fi\/2sin (0 -- — j = one of the m.m.fs. of phase 2iir angle 0 = -- , where i = 0, 1, 2 . . . n — 1, acting in the direc- tion T = - ; that is. the zero point of one of the m.m.fs. FI is n ' taken as zero point of time 0, and the direction of this m.m.f. as zero point of direction T. The resultant m.m.f. in any direction r is thus and, since 2 iir 2 ir\ I 2 ir - — )COB(T-— we have that is, the resultant m.m.f. in any direction T has the phase 6 = r, and the intensity, rcFiA/2 ~^~ thus revolves in space with uniform velocity and constant in- tensity, in synchronism with the frequency of the alternating current. 248 ELEMENTS OF ELECTRICAL ENGINEERING Since in the converter, Fl = ^M, TTU we have the resultant m.m.f. of the power component of the alternating current in the n-phase converter. This m.m.f. revolves synchronously in the armature of the converter; and since the armature rotates at synchronism, the resultant m.m.f. stands still in space, or, with regard to the field poles, in opposition to the direct-current polarization. Since it is equal thereto, it follows that the resultant armature reac- tions of the direct current and of the corresponding power component of the alternating current in the synchronous con- verter are equal and opposite, thus neutralize each other, and the resultant armature polarization equals zero. The same is obviously the case in an inverted converter, that is, a machine changing from direct to alternating current. 94. The conditions in a single-phase converter are different, however. At the moment when the alternating current = 0, the full direct-current reaction exists. At the moment when the alternating current is a maximum, the reaction is the differ- ence between that of the alternating and of the direct current; and since the maximum alternating current in the single-phase converter equals twice the direct current, at this moment the resultant armature reaction is equal but opposite to the direct- current reaction. Hence, the armature reaction oscillates with twice the fre- quency of the alternating current, and with full intensity, and since it is in quadrature with the field excitation, tends to shift the magnetic flux rapidly across the field poles, and thereby tends to cause sparking and power losses. This oscillating reaction is, however, reduced by the damping effect of the mag- netic field structure. It is somewhat less in the two-circuit single-phase converter. Since in consequence hereof the commutation of the single- phase converter is not as good as that of the polyphase con- verter, in the former usually voltage commutation has to be resorted to; that is, a commutating pole used, or the brushes shifted from the position midway between the field poles; and SYNCHRONOUS CONVERTERS 249 in the latter case the continuous-current ampere-turns inclosed by twice the angle of lead of the brushes act as a demagnetizing armature reaction, and require a corresponding increase of the field excitation under load. While the absence of armature reaction eliminates the need of a commutating pole to counteract the sparking due to the re- verse field of armature reaction, nevertheless, commutating poles are very often used in converters, to control the high self- induction of commutation, which economical design requires in such machines. Such commutating poles contain only the am- pere turn required to produce the commutating flux, thus less than in generators. 95. Since the resultant main armature reactions neutralize each other in the polyphase converter, there remain only — 1. The armature reaction due to the small power component of current required to rotate the machine, that is, to cover the internal losses of power, which is in quadrature with the field excitation or distorting, but of negligible magnitude. 2. The armature reaction due to the wattless component of alternating current where such exists. 3. An effect of oscillating nature, which may be called a higher harmonic of armature reaction. The direct current, as rectangular alternating current in the armature, changes in phase from coil to coil, while the alternating current is the same in a whole section of the armature between adjacent leads. Thus while the resultant reactions neutralize, a local effect remains which in its relation to the magnetic field oscillates with a period equal to the time of motion of the armature through the angle between adjacent alternating leads; that is, double frequency in a single-phase converter (in which it is equal in magnitude to the direct-current reaction, and is the oscillating armature reaction discussed above), sextuple frequency in a three-phase converter, and quadruple frequency in a four- phase converter. The amplitude of this oscillation in a polyphase converter is small, arid its influence upon the magnetic field is usually neg- ligible, due to the damping effect of the field spools, which act like a short-circuited winding for an oscillation of magnetism. A polyphase converter on unbalanced circuit can be con- sidered as a combination of a balanced polyphase and a single- phase converter; and since even single-phase converters operate quite satisfactorily, the effect of unbalanced circuits on the 250 ELEMENTS OF ELECTRICAL ENGINEERING polyphase converter is comparatively small, within reasonable limits. Since the armature reaction of the direct current and of the alternating current in the converter neutralize each other, no change of field excitation is required in the converter with changes of load. Furthermore, while in a direct-current generator the arma- ture reaction at given field strength is limited by the distortion of the field caused thereby, this limitation does not exist in a converter; and a much greater armature reaction can be safely used in converters than in direct-current generators, the dis- tortion being absent in the former. The practical limit of overload capacity of a converter is usu- ally far higher than in a direct-current generator, since the arma- ture heating is relatively small, and since the distortion of field, which causes sparking on the commutator under overloads in a direct-current generator, is absent in a converter. The theoretical limit of overload — that is, the overload at which the converter as synchronous motor drops out of step and comes to a standstill — is usually far beyond reach at steady frequency and constant impressed alternating voltage, while on an alternating circuit of pulsating frequency or drooping voltage it obviously depends upon the amplitude and period of the pulsation of frequency or on the drop of voltage.