CHAPTER XXVIII GENERAL POLYPHASE SYSTEMS 266. A polyphase system is an alternating-current system in which several e.m.fs. of the same frequency, but displaced in phase from each other, produce several currents of equal fre- quency, but displaced phases. Thus any polyphase system can be considered as consisting of a number of single circuits, or branches of the polyphase sys- tem, which may be more or less interlinked with each other. In general the investigation of a polyphase system is carried out by treating the single-phase branch circuits independently. Thus all the discussions on generators, synchronous motors, induction motors, etc., in the preceding chapters, apply to single- phase systems as well as polyphase systems, in the latter case the total power being the sum of the powers of the individual or branch circuits. If the polyphase system consists of n equal e.m.fs. displaced from each other by - of a period, the system is called a symmet- rical system, otherwise an unsymmetrical system. Thus the three-phase system, consisting of three equal e.m.fs. displaced by one-third of a period, is a symmetrical system. The quarter-phase system, consisting of two equal e.m.fs. displaced by 90°, or one-quarter of a period, is an unsymmetrical system.- 267. The power in a single-phase system is pulsating; that is, the watt curve of the circuit is a sine wave of double frequency, alternating between a maximum value and zero, or a negative maximum value. In a polyphase system the watt curves of the different branches of the system are pulsating also. Their sum, however, or the total power of the system, may be either con- 396 GENERAL POLYPHASE SYSTEMS 397 stant or pulsating. In the first case, the system is called a balanced system, in the latter case an unbalanced system. The three-phase system and the quarter-phase system, with equal load on the different branches, are balanced systems; with unequal distribution of load between the individual branches both systems become unbalanced systems. \ 0. \/ 1 ^ 0 0 0 0 01 Ac )UBU= 3 k Fig. 192. The different branches of a polyphase system may be either independent from each other, that is, without any electrical inter- connection, or they may be interlinked with each other. In the first case the polyphase system is called an independent system, in the latter case an interlinked system. The three-phase system with star-connected or ring-connected generator, as shown diagrammatically in Figs. 192 and 193, is an interlinked system. Fig. 193. The four-phase system as derived by connecting four equi- distant points of a continuous-current armature with four collector rings, as shown diagrammatically in Fig. 194, is an interlinked system also. The four-wire, quarter-phase system produced by a generator with two independent armature coils, or by two single-phase generators rigidly connected with each other in quadrature, is an independent system. As interlinked system, it is shown in Fig. 195, as star-connected, four-phase system. 398 ALTERNATING-CURRENT PHENOMENA 268. Thus, polyphase systems can be subdivided into: Symmetrical systems and unsymmetrical systems. Balanced systems and unbalanced systems. Interlinked systems and independent systems. The only polyphase systems which have found practical appli- cation are: -E 2 \ ^+E 1 .-fS' 3 ^^ 4 Fig. 194. The three-phase system, consisting of three e.m.fs. displaced by one-third of a period, is used exclusively as interlinked system. The quarter-phase system, consisting of two e.m.fs. in quad- rature, and used with four wires, or with three wires, which may be either an interlinked system or an independent system. The six-phase system, consisting of two three-phase systems in opposition to each other, and derived by transformation from + .E —E nmTswusvsvrno- Fig. 195. a three-phase system, in the alternating supply circuit of large synchronous converters. The inverted three-phase system, consisting of two e.m.fs. dis- placed from each other by 60°, and derived from two phases of a three-phase system by transformation with two transformers, of which the secondary of one is reversed with regard to its primary (thus changing the phase difference from 120° to 180° — 120° = 60°) finds a hmited application in low-tension distribution.