CHAPTER III 



ADDITIONS TO THE THEORY. SECOND APPROXIMATION 



Imperfections of the Theory. Owing to the hypotheses on which 

 is based the preceding elementary theory, in common with all theo- 

 ries concerning alternating current machines, has certain imperfections. 

 We shall discuss these briefly. 



(1) When the currents are not sinusoidal, the results may be mate- 

 rially modified. At this point, it may be stated that we should pre- 

 cisely endeavor to make machines giving sinusoidal currents for power 

 transmission, 1 because, if their E.M.F. do not comprise exactly the 

 same harmonics, the circuit becomes the seat of parasite currents, 

 which are often very important. For example a certain Labour syn- 

 chronous motor having a sinusoidal E.M.F. when run without load, 

 being supplied with current from the distribution system of the Champs 

 Elysees district, where the E.M.F. was non-sinusoidal, required a cur- 

 rent almost double that which it consumed at the factory when supplied 

 from an appropriate generator. This fact, among many others, shows 

 that the effect of harmonics cannot, by any means, be considered 

 negligible. 



(2) The reactance X of the motor is not constant, but varies with 

 the excitation, with the strength of the armature-current, and with its 

 phase-difference with respect to the E.M.F. %. 



In practice, the angle 7- differs sufficiently from 90 to make its 

 variations, under the influence of the preceding effects, very small. 

 Consequently, the line of zero phase-difference, A\N, in Fig. 27, is a 

 curve which is always sufficiently flattened to warrant our continuing, 

 without material error, to compare it to a straight line. But the power- 



1 This question was discussed by various authors in the Electrical World, 

 which had the happy idea of opening its columns to that very interesting con- 

 troversy. The greater portion of those who expressed their opinion, and among 

 them the author of this work, were in accord in recognizing the important 

 advantages of a sinusoidal E.M.F. from various points of view 



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