SYNCHRONOUS MACHINERY 275 



The impedance drop in the armature is 



The generated e.m.f. is, therefore, 



E Q = (E cos 4> - 7r) + j (E sin - 7z ) . . (263) 

 and its absolute value is 



# = V(E cos - 7r) 2 + (E sin - 7z ) 2 . . . (264) 

 This relation can also be obtained by reference to the vector 

 diagram in Fig. 253, c d 



but 



oh = og db = E cos $ 7r, Q 



_T 



and 



hg = oc af = E sin $ Ix Q , 

 therefore, 



E Q = V(E cos < - 7r) 2 + (E sin - 7x ) 2 . 



Fig. 254 represents the compounding curves for unity power 

 factor, 80 per cent power factor leading and 80 per cent lagging. 

 To predetermine these curves the impressed e.m.f. E is main- 

 tained constant, a definite value of power factor is chosen for 

 each curve, the armature current I is varied and the values of E 

 are calculated from equation 264. The values of field current 7/ 

 corresponding to the calculated values of E are obtained from 

 the saturation curve, Fig. 248, and are plotted as ordinates. 



166. Load Characteristics. The power input to the motor 

 armature is the product of the current and the in-phase component 

 of impressed e.m.f.; it is 



Pi = El cos 4> (265) 



The electrical power transformed into mechanical power is the 

 product of the current and the in-phase component of the generated 

 e.m.f.; it is 



P = I(Ecos<f>- Ir} = El cos 0. - 7V, . . (266) 

 and is less than the power input by the armature copper loss. 



The power output is less than the mechanical power developed 

 by the amount of the constant losses in the motor, namely, the iron 

 friction and windage losses; the output, therefore, is 

 P 2 = P constant losses 



= PI 7 2 r constant losses 



= El cos 4> Pr constant losses. . . (267) 



