158 ALTERNATING CURRENTS 



extremely unsafe method, unlike Belm-Eschenburg's, which yields 

 wrong values, but on the safe side. Behrend has termed Eothert's 

 method the optimistic method. 



85. Analysis of Armature Self - inductance into 

 Two Components 



Practical experience having shown that neither of the two methods 

 described yields reliable results, numerous attempts have been made 

 to establish some more satisfactory method. In many of these, the 

 total armature self-inductance is regarded as made up of (1) that 

 portion of the flux due to the armature current which penetrates the 

 field and produces a weakening of it ; and (2) the remaining portion, 

 which is made up of armature leakage lines, i.e. lines linked with 

 the armature windings, but not passing into the field cores, and hence 

 incapable of affecting the main field strength. Where such a splitting 

 up of the total armature self-inductance is adopted, the first portion 

 of the self-inductance is generally spoken of as armature reaction, 

 while the second is termed armature self-inductance (in reality, it is 

 only the leakage self -inductance). 



Looking at the matter from this point of view, and considering 

 the special case in which the armature current lags 90 behind the 

 e.m.f.* when the drop will have its greatest possible value it is 

 obvious that the leakage self-inductance e.m.f. will be simply sub- 

 tracted arithmetically from the open-circuit e.m.f. (the two being in 

 direct opposition of phase), while armature reaction will be equivalent 

 in its effect to a definite reduction in the field ampere-turns. So 

 long as the armature current is constant, both these effects will 

 remain independent of the exciting current. Hence it follows that 

 if we plot, on the same sheet of paper as in Fig. 117 the open- 

 circuit curve OP and the curve LP' connecting the terminal p.d. with 

 the exciting current when the wattless armature current is main- 

 tained constant (by suitably adjusting the reactance which constitutes 

 the load), the two curves will be so related that any point P' on the 

 latter may be obtained from a certain point P on the former by 

 the subtraction of a constant amount PE (representing leakage self- 

 inductance drop) from the e.m.f., and the addition of a constant 

 amount EP' to the field ampere-turns or exciting current (EP' repre- 

 senting the amount required to balance armature reaction). Now, 

 this is equivalent to a bodily displacement of the open-circuit curve 

 through a distance PP'. Thus LP' should simply represent OP 



* This, of course, is an ideal case, as we can never get rid of resistance in the 

 circuit. But with a load of very low resistance and large self-inductance it may be 

 closely approached in practice. 



