TRANSFORMERS 315 



and, therefore, 



V3 1 



= e C D - CCA = -y Eo sin 6 + ^ #o cos 6 



= # sin (0 + 30), 

 = # sin (0-90), 



1 



-- E sin 

 = EQ sin (30 - 0) = E sin + 150. 



Therefore the three e.m.fs. EDA, EAB and EBD are displaced 

 120 degrees in phase and are equal and thus form a three-phase 

 system. 



Under load the e.m.fs. will not be exactly balanced since even 

 at non-inductive load the current in one-half of the winding AB 

 will lead the e.m.f. and in the other half will lag behind it as 

 shown in Fig. 293. 



The power delivered is 



P = C7)-7 1 cos0 + C.7 2 cos(30 + 0) + CA 7 3 cos (30 -6) 

 + ^ El cos (30 + 0) + i#7cos (30 - 0) 



I cos0 + -EI cos0 = V3 El cos0, 



i _ 



and one half of the power is delivered by each transformer. 

 The neutral point of the system is at the centre of the winding 

 FD. 



196. Series Transformer. Series transformers are used to 

 insulate ammeters, wattmeters, relays, etc., from high-voltage 

 circuits, or to reduce the line current to a value suitable for such 

 instruments. In all of these instruments it is very important that 

 the ratio of the currents in the two windings should remain constant 

 throughout the full range. Tn the case of the wattmeter it is also 

 necessary that the primary and secondary currents should be 

 exactly in line, that is, that the phase shift of the transformer 

 should be as small as possible. 



- Fig. 294 and Fig. 295 show vector diagrams for series transformers 

 with the secondaries closed through the meter. The resistance 

 and inductance of the meter are included in the impedance of the 

 transformer. In Fig. 294 the secondary reactance has been taken 

 as double the resistance and in Fig. 295 the resistance is double 



