254 ELECTRICAL ENGINEERING 



cross-magnetizing effect is decreased since a large m.m.f. is re- 

 quired to produce a small change in flux. The demagnetizing 

 m.m.f. increases directly with the current and the leakage factor 

 of the machine also increases and causes a further decrease of the 

 useful flux. 



152. Armature Reactance. The flux produced by the cur- 

 rent in the armature coil in Fig. 229 may be separated into two 

 parts as shown. 



Part (1) is the flux of armature reaction which crosses the gap 

 and interferes with the flux threading the field circuit. Its effect 

 is either cross magnetizing, demagnetizing or magnetizing. 



Part (2) is the flux which only interlinks with the coil itself and 

 does not interfere with the flux produced by the field m.m.f. It 

 is the self-inductive flux of the coil and generates in the coil an 

 e.m.f . of self-inductance, which consumes a component of the e.m.f . 

 generated by rotation. This e.m.f. called the armature reactance 

 drop is equal to the product of the armature current 7 and the 

 armature reactance x and leads the current by 90 degrees. 



The reactance is x = 2wfL, where L is the inductance of the 

 armature. L and x both decrease as the armature current in- 

 creases due to the increased saturation and, therefore, decreased 

 permeability of the leakage path surrounding the armature con- 

 ductors. They also vary as the armature is rotated; when the 

 conductor is under the pole the reluctance of its local leakage 

 path is minimum and L and x are large; when between the poles 

 the reluctance is maximum and L and x are reduced. An aver- 

 age value of x is chosen to represent the armature reactance. At 

 light loads when the current is small the reactance drop will be 

 greater than the value corresponding to the average reactance 

 and when the current is large it will be smaller. 



153. Polyphase Armature Reaction. If n is the number of 

 turns per phase per pair of poles on a two-phase alternator and 

 ii = IQ cos 6 is the current in phase 1 and i 2 = IQ cos (0 90) = 

 I sin 6 is the current in phase 2, the m.m.f. 's of the two phases are 

 mi = nil = nlo cos 6 and m^ = niz = nlo sin 0. These two m.m.f.'s 

 are in quadrature in time and space but combine to give a con- 

 stant m.m.f. nI Q fixed in position relative to the field m.m.f. 

 and revolving synchronously backwards relative to the armature. 

 This can be seen by reference to Fig. 230. AB is the winding 

 of phase 1 and the current is assumed to lag behind the e.m.f. by 



