Xin. Direct-current Converter 105. If n equidistant pairs of diametrically opposite points of a commutating machine armature are connected to the ends of n compensators or autotransformers, that is, electric circuits interlinked with a magnetic circuit, and the centers of these auto- transformers connected with each other to a neutral point as shown diagrammatically in Fig. 140 for n = 3, this neutral is equidis- tant in potential from the two sets of commutator brushes, and such a machine can be used as continuous current converter, to SYNCHRONOUS CONVERTERS 263 transform in the ratio of potentials 1 :2 or 2 : 1 or 1 : 1, in the latter case transforming power from one side of a three- wire system to the other side. Obviously either the n autotransformers can be stationary and connected to the armature by 2 n collector rings, or the auto- transformers rotated with the armature and their common neutral connected to the external circuit by one collector ring. The distribution of potential and of current in such a direct- current converter is shown in Fig. 141 for n = 2, that is, two autotransformers in quadrature. With the voltage 2 e between the outside conductors of the FIG. 140. — Diagram of direct-current converter. system, the voltage between the neutral and outside conductor is ± e, that on each of the 2 n autotransformer sections is e sin(0 — 00 — — J, k = 0, 1, 2 . . . 2 n — 1. Neglecting losses in the converter and the autotransformer, the currents in the two sets of commutator brushes are equal and of the same direction, that is, both outgoing or both incoming, and opposite to the current in the neutral ; that is, two equal currents i enter the commutator brushes and issue as current 2 i from the neutral, or inversely. From the law of conservation of energy it follows that the cur- rent 2 i entering from the neutral divides in 2 n equal and constant branches of direct current, — , in the 2 n autotransformer sections, ' n1 and hence enters the armature, to issue as current i from each of the commutator brushes. 264 ELEMENTS OF ELECTRICAL ENGINEERING In reality the current in each autotransformer section is *7* / irJf \ -- h io \/2 cos ( e — 60 ---- h «) t Ti \ Ti I where iQ is the exciting current of the magnetic circuit of the auto- transformer, and a the angle of hysteretic advance of phase. At the commutator the current on the motor side is larger than the current on the generator side, by the amount required to cover the losses of power in converter and autotransformer. In Fig. 141 the positive side of the system is generator, the negative side motor. This machine can be considered as receiv- ing the current i at the voltage e from the negative side of the system, and transforming it into current i at voltage e on the 21 FIG. 141. — Distribution e.m.f . and current in direct-current converter. positive side of the system, or it can be considered as receiving current i at voltage 2e from the system, and transforming it into current 2 i at the voltage e on the positive side of the system, or of receiving current 2 i at voltage e from the negative side, and returning current i at voltage 2e. In either case the direct- current converter produces a difference of power of 2 ie between the two sides of the three- wire system. The armature reaction of the currents from the generator side of the converter is equal but opposite to the armature reaction of the corresponding currents entering the motor side, and the motor and generator armature reactions thus neutralize each other, as in the synchronous converter; that is, the resultant SYNCHRONOUS CONVERTERS 265 armature reaction of the continuous-current converter is prac- tically zero, or the only remaining armature reaction is that corresponding to the relatively small current required to rotate the machine, that is, to supply the internal losses in the same. The armature reaction of the current supplying the electric power transformed into mechanical power obviously also remains, if the machine is used simultaneously as motor, as for driving a booster connected into the system to produce a difference between the voltages of the two sides, or the armature reaction of the currents generated from mechanical power if the machine is driven as generator. I I. Ill jiHojifljybJU yyyyyyyyyyyyyyywyy jyyyyy a'"o"o a^aza3 C B J1 a"a"a 1J. 2i FIG. 142. — Development of a direct-current converter. 106. While the currents in the armature coils are more or less sine waves in the alternator, rectangular reversed currents in the direct-current generator or motor, and distorted triple-fre- quency currents in the synchronous converter, the currents in the armature coils of the direct-current converter are approximately triangular double-frequency waves. Let Fig. 142 represent a development of a direct-current con- verter with brushes BI and B2, and C one autotransformer re- ceiving current 2 i from the neutral. Consider first an armature coil ai adjacent and behind (in the direction of rotation) an auto- transformer lead 61. In the moment when autotransformer leads 61 62 coincide with the brushes BI B% the current i directly enters 266 ELEMENTS OF ELECTRICAL ENGINEERING the brushes and coil ai is without current. In the next moment (Fig. 142A) the total current i from 61 passes coil ai to brush Bit while there is yet practically no current from 61 over coils a' a", etc., to brush Bz. But with the forward motion of the arma- ture less and less of the current from 61 passes through «i a2, etc., to brush BI and more over a' a", etc., to brush B^ until in the position of a\ midway between 61 and 62 (Fig. 1425), one-half of the current from 61 passes ai a2, etc., to BI, the other half a' a", etc., to B%. With the further rotation the current in a\ grows less and becomes zero when 61 coincides with B%, or half a cycle after its coincidence with BI. That is, the current in FIG. 143. — Current in the various coils of a direct-current converter. coil ai approximately has the triangular form shown as ii in Fig. 143, changing twice per period from 0 to i. It is shown negative, since it is against the direction of rotation of the armature. In the same way we see that the current in the coil a', adjacent ahead of the lead 61, has a shape shown as i' in Fig. 143. The current in coil a0 midway between two commutator leads has the form io, and in general the current in any armature coil ax, dis- tant by angle r from the midway position a0, has the form ix, Fig. 143. All the currents become zero at the moment when the autotrans- former leads 61 62 coincide with the brushes BI B2, and change SYNCHRONOUS CONVERTERS 267 by i at the moment when their respective coils pass a commu- tator brush. Thus the lines A and A' in Fig. 144 with zero values at BI B^ the position of brushes, represent the currents in the individual armature coils. The current changes from A to A' at the moment 0 = r when the respective armature coil passes the brush, twice per period. Due to the inductance of the armature coils, which opposes the change of current, the current waves are not perfectly triangular, but differ somewhat therefrom. With n autotransformers, each autotransformer lead carries the current — , which passes through the armature coils as triangular n current, changing by — in the moment the armature coil passes a commutator brush. This current passes the zero value in the moment the autotransformer lead coincides with a brush. Thus, FIG. 144. — Current in individual coils of a direct-current converter with one compensator. the differents current of n autotransformers which are superposed in an armature coil ax have the shape shown in Fig. 199 for n = 3. That is, each autotransformer gives a set of slanting lines AiA'i, A^A'z, AsA's, and all the branch currents i\, iz, iz, super- posed, give a resultant current ix, which changes by i in the moment the coil passes the brush. ix varies between the extreme values £ (2 p — 1) and ^(2p + 1), if the armature coil is dis- placed from the midway position between two adjacent autotrans- former leads by angle r, and p = - • p varies between — ^— and Thus the current in an armature coil in position p = - can 268 ELEMENTS OF ELECTRICAL ENGINEERING be denoted in the range from p to 1 + p, or r to TT + r, by where e x = - 7T \\ / "1?t A'f A", / A"2 A FIG. 145. — Current in a single coil of a direct-current converter with three compensators. The effective value of this current is / = Since in the same machine as direct-current generator at voltage 2 e and current i] the current per armature coil is ~> the ratio of current is I i 2 SYNCHRONOUS CONVERTERS 269 and thus the relative Pr loss or the heat developed in the armature coil, /A2 *- i with a minimum, and a maximum, p = 0, TO = M> 1 ^ 1 = — ' Jm 3^w2 3w2 The mean heating or Pr of the armature is found by integrating over 7 from 1 1 as r = n J_ 2n ydp 2n I_L JL^ _ 1 + n2 3n2 ' This gives the following table, for the direct-current converter, of minimum current heating, 70, in the coil midway between DIRECT-CURRENT CONVERTER IV RATING d. c. No. of compensators, n = gen. 1 2 3 4 n 00 Minimum current heating P = 0, 70 = 1 ' K K H H H H Maximum current heating, 1 i 1 % J^2 ^ i^g /^ n' n Mean current heating, 1 r = 1 H ^2 !%7 1%8 H Rating, 1 Vr" 1 1.225 1.549 1.643 1.681 / 3n2 1.732 \l+n2 270 ELEMENTS OF ELECTRICAL ENGINEERING adjacent commutator leads, maximum current heating, ym, in the coil adjacent to the commutator lead, mean current heating, r, and rating as based on mean current heating in the armature, 1 . As seen, the output of the direct-current converter is greater than that of the same machine as generator. Using more than three autotransformers offers very little advantage, and the dif- ference between three and two autotransformers is comparatively small, also, but the difference between two and one autotransfor- mer, especially regarding the local armature heating, is considera- ble, so that for most practical purposes a two-autotransformer converter would be preferable. The number of autotransformers used in the direct-current converter has a similar effect regarding current distribution, heating, etc., as the number of phases in the synchronous converter. Obviously these relative outputs given in above table refer to the armature heating only. Regarding commutation, the total current at the brushes is the same in the converter as in the generator, the only advantage of the former being the better commutation due to the absence of armature reaction. The limit of output set by armature reaction and correspond- ing field excitation in a motor or generator obviously does not exist at all in a converter. It follows herefrom that a direct- current motor or generator does not give the most advantageous direct-current converter, but that in the direct-current converter just as in the synchronous converter, it is preferable to propor- tion the parts differently in accordance with above discussion, as, for instance, to use less conductor section, a greater number of conductors in series per pole, etc.