148 ALTERNATING CURRENTS 



of armature reaction. (The voltage actually induced is E', Fig. 

 152.) However, if the effect of the armature reaction is replaced 

 by an armature reactance drop, the voltage EI may be considered 

 as being entirely used in sending the current I\ through the arma- 

 ture impedance. That is, 



where Z 8 is the synchronous impedance 

 of the armature. This short-circuit con- 

 dition is represented vectorially in Fig. 

 152, where /i is the short-circuit current 

 >i l and EI the assumed internal emf. of the 

 armature. The synchronous impedance 



FIG 152. Short-circuit vec- dro is made Q f twQ components, /i#, 

 tor diagram of an alternator. x 



where R is the effective resistance of the 



armature, and IiX s , where X 8 is the synchronous reactance of 

 the armature. 



E 

 Obviously, Z 8 = - 1 (41) 



and X s = VZ 8 * - R 2 (42) 



In practice R is small compared with Z 8 and they combine 

 almost in quadrature so that 



E7 



X a = -,- very nearly. 

 ^i 



The value of the synchronous reactance depends to a large 

 extent upon the degree of saturation of the iron. For example, 

 at low saturation the armature mmf. will have a much greater 

 effect on the magnetic circuit than if the iron were saturated. 

 Therefore, under short-circuit conditions, where the iron is oper- 

 ating at low saturation, the synchronous reactance will be too 

 large. The variation of synchronous impedance with field cur- 

 rent is shown in Fig. 151. As the iron becomes more saturated, 

 the synchronous impedance decreases. Under operating condi- 

 tions, the iron is considerably more saturated than it is under 

 short-circuit conditions. In order to approach as near as possible 

 to operating conditions, it is desirable to obtain the synchronous 

 impedance at the highest possible value of armature current, as 

 at /i, Fig. 151. Also, the synchronous impedance is determined 

 at very low power-factor, corresponding to short-circuit condi- 



