222 



ELEMENTS OF ELECTRICAL ENGINEERING. 



connected or F-connected to the supply mains, and in either 

 case the secondary coils may be A-connected or K-connected 

 to the service mains, so that four arrangements are possible, 

 namely, the AA-connection, the A ^connection, the FA-con- 

 nection, and the FF-connection. The AA-connection is, how- 

 ever, the usual arrangement, for, in this case, the system remains 

 operative when one of the transformers is disconnected ; thus 

 with the AA-connection the burning-out of one of the trans- 

 formers need not render the system inoperative, although the two 

 remaining transformers would operate at a disadvantage, not only 

 because the two transformers would have to carry the load of 

 three, but because the currents in the two transformers are in- 

 creased in a greater ratio than 2 : 3 as explained in the following 

 paragraph. 



The use of two transformers for three-phase transformation. Figure 187 shows 

 the connections of two transformers Aa and Bb for three-phase transformation. It 

 is at once evident that this arrangement maintains the proper voltage (proper, that is, 

 in value and in phase) between service mains I and 2, and the proper voltage be- 

 tween service mains 2 and 3 ; but a proper voltage between I and 2 and a proper 

 voltage between 2 and 3 gives necessarily a proper voltage between 3 and I. 



Supply main I 



Supply malm 



Supply main 3 



service main i 



Fig. 187. 



Suppose that the service mains are delivering current to three similar A-connected 

 receiving circuits, each current lagging 6 behind the corresponding voltage, as shown 

 in Fig. 1 88. The lines I v 1^ and / 3 represent the currents in the respective re- 

 ceiving circuits, so that the power delivered to each receiving circuit is El cos 6 where 



E is used for the common numerical value of E ly 2 and 

 the common numerical value of J v 7 2 and 7 3 . 



/ is used for 



