260 ELECTRICAL ENGINEERING 



The effects of single-phase armature reaction are relatively 

 greater in machines with a small number of turns on the fields, as 

 turbo alternators. 



155. Electromotive Forces in the Alternator. In studying 

 the performance of an alternator it is necessary to determine the 

 relation between the terminal e.m.f. E, the e.m.f. E\ generated by 

 rotation and the e.m.f. E generated at no load. 



Ei is the e.m.f. generated in the armature by the rotation of the 

 flux produced in the air gap by the resultant of the magneto- 

 motive forces of the field and armature. It is the vector sum of 

 the terminal e.m.f. E and the e.m.f. consumed by the impedance 

 of the armature. The armature impedance is z = Vr 2 + x 2 , or 

 expressed in rectangular coordinates z = r + jx, where r is the 

 resistance of the armature and consumes a component of e.m.f. 

 Ir in phase with the current 7, and x is the true self-inductive 

 reactance of the armature and consumes a component of e.m.f. 

 Ix in quadrature ahead of the current. 



The generated e.m.f. thus is 



E l = E + Iz 



= E+I\r+jx), ..... (252) 



and the terminal e.m.f. is the vector difference between the e.m.f. 

 generated in the armature by rotation and the impedance drop 

 E = Ei-I(r+jx) ...... (253) 



EQ is the e.m.f. generated at no load due to cutting the flux pro- 

 duced by the field m.m.f . Mf acting alone. Under load current flows 

 in the armature and exerts a m.m.f. M a , which is either cross mag- 

 netizing, demagnetizing or magnetizing depending on the phase 

 relation of the current and the terminal e.m.f. This armature 

 m.m.f. combines with the field m.m.f. and changes both the intensity 

 and the distribution of the flux in the gap, so that under load the 

 e.m.f. generated in the armature is not the same as at no load. 



The difference between the two is the e.m.f. consumed or the 

 e.m.f. not generated due to the presence of the armature reactance. 

 This e.m.f. is proportional to the current and can be expressed as 

 the product of the current 7 and a component of reactance x' . It 

 is Ix' and is in quadrature ahead of the current. Thus 



= E + I ( r +jx)+jlx f 

 = E+ I \r+j(x + x')\ 

 = E+I(r+jx ) ........ (254) 



