144 SYNCHRONOUS MOTORS 



The expression for the mean electric power can be easily obtained, 

 according to the usual rule, by multiplying the vector S by the pro- 

 jection of I on S (I and 5 being effective values). We then have 



P-SIco&ACB 



= I 2 aj cos (TT ( 



on the assumption that 



(/' ) cos d> 

 2/ 



tan d= 



The value of the power-factor, obtained from the preceding, is 



cos (7c <l>d)= cos </> cos d+sin <j> sin d 

 A cos sin (> 



vi\ 2 



+- sin 



2 



A sin 

 or 



4 



. . . . 

 whence P= toAl 2 sin w cos </>= 



The power is negative and therefore the alternator operates as a 

 motor (consuming electrical energy and producing mechanical power) 



when the value of ^ is comprised between o and ; and it operates 

 as generator (producing electrical energy and consuming mechanical 

 power) for values of ^ comprised between o and --- , i.e., when the 



current is leading. 



The power is a maximum for 



and its absolute value is 



_ 



f max 



2 2 



