COUPLING OF POLYPHASE CIRCUITS 35 



OA and OB', i.e. to the projection of OL. IJut since OL m 20A. cos 

 30 SB y/3 . OA, we see that, with a balanced system having a star 

 coupling and supplied with sine waves of e.m.f., tlie line p.d. is equal 

 to y'S, or 1*732 times the phase p.d. 



Another method of coupling three-phase circuits is that shown in 

 Ki;, r . 26, and known as the mesh or triangle or delta method. It is 

 immediately obvious that the line p.d. is 

 now equal to the phase p.d. The line 

 currents, however, are not equal to the 

 phase currents, each line current being 

 at any given instant equal to the difference 

 of the adjacent phase currents as is at 

 once evident from Fig. 26. Hence the 

 vector diagram of Fig. 25 (6) is now appli- 

 cable to the currents, and we see that 

 with a mesh grouping and simple sine 



waves the line current is equal to \/3, or 1*732 times the phase current. 

 The advantage of coupling the circuits will now be readily under- 

 stood. For if in Fig. 26 the three circuits had been kept separate, 

 six Hue wires, each, we shall suppose, of cross-section a, would have 

 been required (two wires for each phase or circuit). By coupling 

 the circuits delta fashion, so as to maintain the original p.d. across 

 each pair of mains unaltered, the number of wires is reduced to three, 

 and the cross-section of each is, for the same current density as 

 before, ^/3 . a. Thus the ratio of the amount of copper in the 



coupled circuits to that in the uncoupled ones is - - = ^- 



1*732 



= = 0'866, representing a saving of about 13 per cent., and this 



2i 



saving represents a clear gain, the coupling of the circuits not being 

 attended with any disadvantages such as result, for example, from 

 the coupling of two-phase circuits. In the latter case, the maximum 

 p.d. between the two outer line wires is ^/2, or 1*414 times the phase 

 p.d., which either increases the risk of a breakdown or else necessitates 

 better and hence more expensive insulation for the line than would 

 be necessary if the circuits were kept separate. 



As regards the practical use of the two methods of coupling three- 

 phase circuits, it may be said that the coils of generators and motors 

 are generally coupled star fashion, while transformers are, for reasons 

 to be explained later, in most cases delta-connected. Rotary converters 

 are, from the nature of the case, also delta-connected ; and so is an 

 ordinary lamp load. 



