CHAPTER XXV. GENERAL POLYPHASE SYSTEMS. 260. A polyphase system is an alternating-current sys- tem in which several E.M.Fs. of the same frequency, but displaced in phase from each other, produce several currents of equal frequency, but displaced phases. Thus any polyphase system can be considered as con- sisting of a number of single circuits, or branches of the polyphase system, 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 1 / n of a period, the system is called a symmetrical 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. 261. The flow of power in a single-phase system is pulsating ; that is, the watt curve of the circuit is a sine GENERAL POLYPHASE SYSTEMS, 431 wave of double frequency, alternating between a maximum value and zero, or a negative maximum value. In a poly- phase system the watt curves of the different branches of the system are pulsating also. Their sum, however, or the total flow of power of the system, may be either constant 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 sys- tems ; with unequal distribution of load between the indi- vidual branches both systems become unbalanced systems. Fig. 181. Fig. 182. The different branches of a polyphase system may be either independent from each other, that is, without any electrical interconnection, 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 inter- linked system. The three-phase system with star-connected or ring-con- nected generator, as shown diagrammatically in Figs. 181 and 182, is an interlinked system. 432 ALTERNATING-CURRENT PHENOMENA. The four-phase system as derived by connecting four equidistant points of a continuous-current armature with four collector rings, as shown diagrammatically in Fig. 183, Fig. 183. 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. 184, as star-connected four-phase system. -E r Fig. 184. 262. 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 application are : The three-phase system, consisting of three E.M.Fs. dis- GENERAL POLYPHASE SYSTEMS. 433 placed by one-third of a period, used exclusively as inter- linked system. The quarter-phase system, consisting of two E.M.Fs. in quadrature, and used with four wires, or with three wires, which may be either an interlinked system or an indepen- dent system. The six-phase system, consisting of two three-phase sys- tems in opposition to each other, and derived by transforma- tion from a three-phase system, in the alternating supply circuit of large synchronous converters. The inverted three-phase system, consisting of two E.M.F.'s displaced 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 limited application in low tension distribution. 434 ALTERNATING-CURRENT PHENOMENA.