ALTERNATOR REGULATION AND OPERATION 139 



not by the generator voltage. Therefore, when the current lags, 

 this impedance triangle swings clockwise with the current. 



As before, the impedance drop may be added at the end of 1'. if 

 t he proper phase relat ions are observed. The most direct method 

 of finding the induced emf. E' is to use the method described 

 under the triangle of vectors, page 12. IR, which is in phase 

 with the current, is first added vectorially at the end of the ter- 



I i.. 14."*.- Alternator vector diagram for power-factor cos 6, current lagging. 



minal voltage V. Then the reactance drop IX, at right angles 

 to the current and leading, is added at the end of IR. The 

 resultant voltage found by completing the polygon is the induced 

 emf. A'/ This method is illustrated in Fig. 145 (6), where //.' is 

 parallel to 7 and IX is at right angles to 7 and leading. The 

 geometrical solution of this diagram is quite simple. If 1 1\ is 

 projected on the current vector 7, a right triangle of voltages, 

 OW. is formed, of which E' is the hypotenuse. The values of the 

 two legs of this right triangle may be found as follows: 



Oa = V cos 

 ab = IR 



aV = be = Fsin 

 cd = /A 



E' = V0F' + ~W = V(0a + a&) 2 + (be + cd) 

 = V(V cos + //?)' + (V sin + IX)* 



The mi-rent now lag- the induced voltage /'' by t he angle , '. 

 which can be readily determined. 



, _ h,l \ (fa +IX 

 <>!> I COB0 + IR 



