VECTOR DIAGRAM OF GENERATOR 



221 



130. Vector Diagram of e.m.f.'s and its Trans- 

 formation 



We may next, in order to reduce the stator and rotor currents to 

 the same frequency ( 106), imagine the negative slip increased, and 

 at the same time resistances introduced into the rotor circuits so as 

 to maintain the current and phase difference unaltered, until the slip 

 becomes numerically equal to unity, i.e. until the speed is double 

 that of synchronism. If the 

 original slip was numerically 

 equal to s, then, r a denoting the 

 original resistance of one phase 

 of the rotor circuit i.e. the re- 

 sistance of the short-circuited 

 phase and Ila the required 

 equivalent resistance for a 

 negative slip of unity, we must 



7*o 



have E 2 = . For, by increas- 

 s 



ing the slip in the ratio 1 : s, 

 we have increased the hypo- 

 thetical rotor e.m.f. and the 

 rotor reactance in this ratio, so 

 that in order to have the current 

 and its phase relatively to the 

 e.m.f. unaltered, the total resist- 

 ance must also be increased in 

 the same ratio. If, as before, r 

 denote the added external resist- 

 ance to each rotor phase, r = Ra 



-r2 = l ^- S r 2 (cf. 106). 



o 



The currents in the two 

 windings having by this artifice 

 been reduced to the same fre- 

 quency, we may proceed to 

 construct the vector diagram 



of e.m.f.'s similar to the motor diagram shown in Fig. 127. The 

 lines OA = rJi and AB = pLili remain unaltered in phase. But 

 the vector r^L* of the secondary drop must, in accordance with 

 diagrams (c) and (d) of Fig. 140, be shifted forward (i.e. in the 

 counter-clockwise direction) by an amount TT + 2o, so as to occupy 

 the position OD shown in Fig. 141, the angle DOE being equal to 



FIG. 141. Vector Diagram of Induction 

 Generator. 



