306 



ELECTRICAL ENGINEERING 



185. Regulation. The regulation of a transformer is very 

 much better than that of an alternator because the e.m.fs. con- 

 sumed by the leakage reactances are very much smaller. If the 

 terminal e.m.f. at full load is taken as 100 per cent and the imped- 

 ance drop is expressed in per cent the sum of the two in their proper 

 phase relation gives the terminal e.m.f. at no load in per cent. 



Using rectangular coordinates and taking the secondary current 

 as the real axis, the impedance drop in per cent is E D = Ir per 

 cent + jlx per cent ; the secondary terminal voltage at full load is 

 E = 100 cos 6 -{- j 100 sin 6; the secondary terminal voltage at no 

 load is E 2 = E + E D = 100 cos + Ir per cent + j (100 sin + Ix 

 per cent), 

 and in absolute values 



and 



E 2 = V(100 cos 6 + Ir%Y + (100 sin + Ix%) 2 . (292) 

 E = 100. 



Therefore, the per cent regulation for the load power factor cos 6 

 is E 2 - E = E 2 - 100. 



Fig. 280 shows a regulation curve plotted on a power-factor base. 

 For leading power factors the regulation becomes negative, that is, 

 the voltage rises with load. 



-i 



80 100 



Lag 



G) 



Ldad 



Percent Power Factor 



FIG. 280. Regulation curve of a transformer. 



186. Losses in Transformers. The losses in a transformer 

 are the copper losses and the iron losses. 

 The copper loss is 



W c = 7M + / 2 V 2 (293) 



and is almost evenly divided between the primary and the second- 

 ary since the two windings are designed for approximately the same 



