I. General 82. For long-distance transmission, and to a certain extent also for distribution, alternating currents, either polyphase or single-phase, are extensively used. For many applications, however, as especially for electrolytic work, direct currents are required, and are usually preferred also for electrical railroading and for low-tension distribution on the Edison three- wire system. Thus, where power is derived from an alternating system, transforming devices are required to convert from alternating to direct current. This can be done either by a direct-current generator driven by an alternating synchronous or induction motor, or by a single machine consuming alternating and pro- ducing direct current in one and the same armature. Such a machine is called a converter, and combines, to a certain extent, the features of a direct-current generator and an alternating synchronous motor, differing, however, from either in other features. Since in the converter the alternating and the direct current are in the same armature conductors, their e.m.fs. stand in a definite relation to each other, which is such that in practically all cases step-down transformers are necessary to generate the required alternating voltage. Comparing thus the converter with the combination of syn- chronous or induction motor and direct-current generator, the converter requires step-down transformers; the synchronous motor, if the alternating line voltage is considerably above 10,000 volts, generally requires step-down transformers also; with voltages of 1000 to 10,000 volts, however, , usually the synchronous motor and frequently the induction motor can be wound directly for the line voltage and stationary transformers saved. Thus on the one side we have two machines with or sometimes without stationarytransformers, on the other side a single machine with transformers. Regarding the reliability of operation and first cost, obviously a single machine is preferable. 223 224 ELEMENTS OF ELECTRICAL ENGINEERING Regarding efficiency, it is sufficient to compare the converter with the synchronous-motor-direct-current-generator set, since the induction motor is usually less efficient than the syn- chronous motor. The efficiency of stationary transformers of large size varies from 97 per cent, to 98 per cent., with an average of 97.5 per cent. That of converters or of synchronous motors varies between 91 per cent, and 95 per cent., with 93 per cent, as average, and that of the direct-current generator between 90 per cent, and 94 per cent., with 92 per cent, as average. Thus the converter with its step-down transformers will give an average efficiency of 90.7 per cent., a direct-current generator driven by synchronous motor with step-down transformers an efficiency of 83.4 per cent., without step-down transformers an efficiency of 85.6 per cent. Hence the converter is more efficient, and there- fore is almost always preferred. Mechanically the converter has the advantage that no transfer of mechanical energy takes place, since the torque consumed by the generation of the direct current and the torque produced by the alternating current are applied at the same armature con- ductors, while in a direct-current generator driven by a syn- chronous motor the power has to be transmitted mechanically through the shaft. EC. Ratio of e.m.fs. and of Currents 83. In its structure the synchronous converter consists of a closed-circuit armature, revolving in a direct-current excited field, and connected to a segmental commutator as well as to collector rings. Structurally it thus differs from a direct- current machine by the addition of the collector rings, from certain (now very little used) forms of synchronous machines by the addition of the segmental commutator. In consequence hereof, regarding types of armature windings and of field windings, etc., the same rule applies to the converter as to all commutating machines, except that in the converter the total number of armature coils with a series-wound armature, and the number of armature coils per pair of poles with a multiple- wound armature, must be divisible by the number of phases, and that multiple spiral and reentrant windings are difficult to apply. Regarding the wave shape of the alternating counter-gener- SYNCHRONOUS CONVERTERS 225 ated e.m.f., similar considerations apply as for a synchronous machine with closed-circuit armature; that is, the generated e.m.f. usually approximates a sine wave, due to the multi-tooth distributed winding. Thus, in the following, only those features will be discussed in which the synchronous converter differs from the commu- tating machines and synchronous machines treated in the preceding chapters. Fig. 122 represents diagrammatically the commutator of a direct-current machine with the armature coils A connected to adjacent commutator bars. The brushes are BiB2, and the field poles FiF2. If now two oppositely located points a ia2 of the commutator are connected with two collector rings DiD2, it is obvious that '8 FIG. 122. — Single-phase converter commutator. the e.m.f. between these points aia2, and thus between the collector rings DiZ>2, will be a maximum in the moment when the points aia2 coincide with the brushes BiB2, and is in this moment equal to the direct voltage E of this machine. While the points ai3 and D4 an alter- nating voltage of the same frequency and intensity will be produced as between DI and D2, but in quadrature therewith, since at the moment where a3 and a4 coincide with the brushes BiB2 and thus receive the maximum difference of potential, ai and az are at zero points of potential. Thus connecting four equidistant points a\, a2, 0,3, a4 of the SYNCHRONOUS CONVERTERS 227 direct-current generator to four collector rings D\, D2, D3, D4, gives a four-phase converter of the e.m.f. EI = —= E per phase. v 2 The current per phase is (neglecting losses and phase displace- ment) since the alternating power, 2 EJi, must equal the direct-current power, EI. Connecting three equidistant points of the commutator to three collector rings as in Fig. 124 gives a three-phase converter. 85. In Fig. 125 the three e.m.fs. between the three collector rings and the neutral point of the three-phase system (or Y voltages) are represented by the vectors OEi, OEZ, OEs, thus FIQ. 124.— Three-phase syn- chronous converter. FIQ. 125. — E.m.f. diagram of three-phase converter. the e.m.f. between the collector rings or the delta voltages by vectors EiE2, E2E3, and E$E\. The e.m.f. OEi is, however, nothing but half the e.m.f. EI in Fig. 122, of the single-phase Tjl converter, that is, = - = - Hence the Y voltage, or voltage 2 v 2 between collector ring and neutral point or center of the three- phase voltage triangle, is — -= = 0.354 E. 2V2 and thus the delta voltage is E' = El V3 0.612 E. 228 ELEMENTS OF ELECTRICAL ENGINEERING Since the total three-phase power 3 IiEi equals the total continuous-current power IE, it is In general, in an n-phase converter, or converter in which n equidistant points of the commutator (in a bipolar machine, or n equidistant points per pair of poles in a multipolar machine with multiple-wound armature) are connected to n collector rings, the voltage between any collector ring and the common neutral, or star voltage, is consequently the voltage between two adjacent collector rings, or ring voltage, is s' E sin- V2 since — is the angular displacement between two adjacent col- lector rings. Herefrom the current per line, or star current, is found as 2V27 and the current from line to line, or from collector ring to ad- jacent collector ring, or ring current, is V2/ r = . 7T n sin — n 86. As seen in the preceding, in the single-phase converter consisting of a closed-circuit armature tapped at two equi- distant points to the two collector rings, the alternating voltage is —-= times the direct-current voltage, and the alternating cur- V 2 _ rent \/2 times the direct current. While such an arrangement of the single-phase converter is the simplest, requiring only two collector rings, it is undesirable, especially for larger machines, on account of the great total and especially local 7V heating in the armature conductors, as will be shown in the following, and SYNCHRONOUS CONVERTERS 229 due to the waste of e.m.f., since in the circuit from collector ring to collector ring the e.m.fs. generated in the coils next to the leads are wholly or almost wholly opposite to each other. The arrangement which I have called the two-circuit single- phase converter, and which is diagrammatically shown in Fig. 126, is therefore preferable. The step-down transformer T contains two independent secondary coils A and B, of which one, Ay feeds into the armature over conductor rings DiD2 and leads dia2, the other, B, over collector rings D3Z>4 and leads a3a4, so that the two circuits aiaz and a3a4 are in phase with each other, and each spreads over 120 deg. arc instead of 180 deg. arc as in the single-circuit single-phase converter. a* FIG. 126. — Two-circuit single-phase converter. In consequence thereof, in the two-circuit single-phase con- verter the alternating counter-generated e.m.f. bears to the con- tinuous-current e.m.f. the same relation as in the three-phase converter, that is, and from the equality of alternating- and direct-current power, 2 /i#i = IE, it follows that each of the two single-phase supply currents is -v/2 If = -I = 0.8177. It is seen that in this arrangement one-third of the armature, from ai to a3 and from a2 to a4, carries the direct current only, the other two-thirds, from ai to a2 andfroma3to a4, the differential current. x5 230 ELEMENTS OF ELECTRICAL ENGINEERING A six-phase converter is usually fed from a three-phase system by three transformers or one three-phase transformer. These transformers can either have each one secondary coil only of E twice the star or 7 voltage, = —T=> which connects with its two terminals two collector rings leading to two opposite points of the armature, or each of the step-down transformers contains two independent secondary coils, and each of the two sets of secondary coils is connected in three-phase delta or F, but the one set of coils reversed with regard to each other, thus giving two three-phase systems which join to a six-phase system. The different transformer connections then are distinguished as "diametrical/7 "double delta" and "double F." For further arrangements of six-phase transformation, see "Theory and Calculation of Alternating-current Phenomena/7 fourth edition, Chapter XXXVI. The table below gives, with the direct-current voltage and direct current as unit, the alternating voltages and currents of the different converters. -u •** 11 11 1! V § 43 A i 1 f 1 A dve-phase 1 " w fl.S §2 ,rj § i •a 08 °° hj H £ 00 H * i 1 i 1 i 1 1 i Volts between collector 2\/2 2V2 2V2 2-S/2 2V2 2V2 2\/2 ring and neutral point. = 0 . 354 = 0.354 = 0 . 354 = 0.354 = 0.354 = 0 . 354 = 0 . 354 1 V3 V3 1 . Tf sin — Volts between adjacent collector rings 1.0 V2 = 0.707 2V2 = 0.612 2V2 = 0.612 ^=0.5 2V2 = 0.354 0.183 n vl Amperes per line V2 2-S/2 1 V2 2"V^2 V2 V3 3 V2 3 n 1.0 = 1.414 = 0.817 = 0.943 = 0 . 707 = 0.472 0.236 Amperes between ad- jacent lines V2 V2 V3 2V 2 3V3 V2 3 . n . IT = 1.414 = 0.817 = 0.545 ^ = 0.5 = 0.472 0.455 n These currents give only the power component of alternating current corresponding to the direct-current output. Added thereto is the current required to supply the losses in the machine, that is, to rotate it, and the wattless component if a phase dis- placement is produced in the converter. SYNCHRONOUS CONVERTERS 231