206 GENERAL DIAGRAMS FOR SYNCHRONOUS MOTORS 



responding current values, /, and Id, of the converter, and, in particular, 

 the loads dD, dD', dD". ... If the required characteristic has already 

 been drawn by points, for the same values of e, E', e", . . ., the compar- 

 ison of the two curves will show at once the discrepancies between 

 the values wanted and those which the apparatus can give. 



The objection to this diagram is that the circles, in practice, cut the 

 QP right lines at very sharp angles, and that the points of intersection 

 are somewhat uncertain, i.e., it is difficult to locate them accurately. 



In order to make the comparison with greater precision by calcula- 

 tion, the value of /, is calculated, as a function of e, by Eqs. (2) and 

 (29), namely, 



E 2 - 2 , ... (2) 



(nkn\.. KN' T 



( / =)(I w -jo')+=I=A-A d ...... (29) 



\V2/ V2 



These two equations, containing two unknown quantities, I w and I d , 

 enable I d to be eliminated, and a solution to be obtained for /, in terms 

 of known quantities, e being supposed to have been previously deter- 

 mined. This calculation, though a trifle tedious, presents no difficulties. 



The conditions of operation in various cases can be easily pre- 

 determined without drawing the curve accurately. Since, from what 

 precedes, the angle of the PQ phase-lines depends on the reactive 

 current io permitted at zero load, it will be apparent that the choice 

 of values for this current should be made with the idea of making the 

 actual curve agree as closely as possible with the desired curve. The 

 principal practical cases will be investigated from this standpoint. 



Application in the Case of Separate Excitation. Let us suppose, 

 at first, for the sake of greater simplicity, that the shunt-excitation 

 is replaced by a separate excitation which is constant. A d is then 

 constant. It is seen, immediately, that if no series-winding is added, 

 the converter can only give a decreasing voltage as the load increases. 

 The lag-characteristic for all loads is, in fact, a right line, PQ, parallel 

 to BY (Fig. 22); and if we take, on that line, points C'C", whose 

 distance from P increases, the circles of constant radius, E, cut the 

 axis BO at points O, O', O", which come nearer to B; hence, the volt- 

 ages proportional to OB are decreasing. 



Therefore, whatever may be the reactance and the value selected 

 for the external E.M.F. E, it is not possible to maintain the voltage 

 constant at the brushes on the direct-current side, with a separate excita- 

 tion, and still less so with a shunt-excitation. It goes without saying 



