SYNCHRONOUS MACHINERY 237 



are 120 degrees out of phase with one another. If the effective 

 value of the current in each of the lines is represented by I t then 

 I, = I A = I B = I c = V3 /. 



The effective values of all these quantities are shown in the vector 

 diagram in Fig. 204. 



The power supplied by the alternator is 



P = EI /i cos + E z Iz cos <t> + E 3 h cos (j> 



= 3 El cos <f> (240) 



= V3 EJi cos (241) 



and is equal to A/3 times the product of the terminal e.m.f., the 

 line current and the power factor. 



FIG. 205. 



If the system is not balanced, that is, if either the currents or 

 the power factors in the three phases differ from one another the 

 line currents will not be equal and they will not be displaced in 

 phase by 120 degrees. 



If the current in phase 1 is 



i'i = J 0l sin (6 - fa) 

 and the current in phase 2 is 



i z = J 02 s in (B - </> 2 - 120) 



the current in line A is 



iA = ii ^ 



= J 0l sin(0 - $1) - 7 , sin (0 - fa - 120). . (242) 



Fig. 205 shows a " Y "-connected three-phase system. 



Using the same notation as before and taking the results ob- 

 tained in Art. 141, 



