THE S] \Cf{RONOUS MOTOR 



317 



low values of fiold current, the armature current is large and is 



lapsing. As the field current is increased, the power-factor 



uses and the armature current decreases until it reaches its 



minimum value /i. If the field current be still further increased, 



muiture current begins to increase and becomes leading. 



In other words, the motor passes from under-excitation to over- 



extitatian when the field current is increased from a low to a high 



value. 



The current /i is the value of the current at unity power-factor. 

 This is illustrated in Fig. 294. Let 7 2 

 })< the value of line current for some 

 power-factor, cos 2 . The power (for 

 one phase) is, 



p l = V'h cos 2 



where V is the phase voltage. 

 But 



(7, cos 2 ) = /! 72) 



for all values of 2 . 



In other words, for constant power 

 PI, /i is always the energy component 

 of the current regardless of the power- 

 factor. Therefore, the current vector 



' 



I 



X 



FIG. 294. Vector diagram 

 Will always terminate On the lineAA showing current variation iii 



perpendicular to V. The current synchronous motor with con- 

 . . stant power input. 



is a minimum at /i, where the cur- 

 rent is in phase with V '. The power-factor is then unity. The 

 exeitation corresponding to the armature current I\ is called 

 ormal excitation of the motor for the load in question. For 

 an exrjtation less than the normal value, the motor take- a 

 :/ current and is said to he nnth-r-i'jrcitnl; for values of the 

 than the normal value the motor takes a 

 leading current and is said to lie over-excited. 



By aid of the V-curves, the power-factor for any other value 



of line current and given input may be obtained. For example, 



assume that it is desired to obtain the power-factor fm- some value 



i,' / Prom Fig, -'.M. the power-factor 



cos 2 = /-. / Therefore, the power-factor for any current /. 



may be found by dividing the current / into the minimum or 



