EFFECT OF HARMONICS ON THE TRANSMISSION OF POWER 281 



original period. This may occur accidentally and cause many curious 

 results in the working of motors. 



It is, then, of the first importance in the transmission of power that 

 the curves shall be pure sine curves, and dynamos, 3 transformers and 

 motors must be designed in the future with reference to this point. 

 It would seem, also, that most calculations on the efficiency of power 

 transmission by alternating currents must be at fault unless they 

 include the action of the harmonics. 



As to the amount of loss from this cause it is difficult to decide in 

 general. With synchronous motors the harmonics simply flow around 

 the wires without producing useful current of any kind. But this may 

 not cause great loss if the resistance is small. Indeed, considerable 

 distortion may represent small loss of power in certain cases and great 

 loss in others, according to the difference of phase of the current and 

 electromotive force in the harmonics. 



In the case of motors with rotary fields the harmonics produce fields 

 revolving with velocities 3, 5, 7, etc., times the primary field. Now it 

 is essential for the efficiency of these motors that the armature shall 

 revolve nearly as fast as the field, and hence the efficiency for the 

 harmonics must be very small indeed, and this must decrease the effi- 

 ciency of the apparatus as a whole. 



As to the heating of the wires by the harmonics, it is easy to see that 

 the total heating due to all the currents of different periods will simply 

 be the sum of the heatings due to each of the currents separately. 



The effect of harmonics on the hysteresis is much more complicated 

 and can hardly be calculated without further experiment. However, 

 the following hypotheses may give some idea of the action. Let the 

 primary electromotive force be considered unity, and let a 3 , a 5 , etc., be 

 the electromotive forces of the harmonics. If these acted separately 

 on the hysteresis the total would be : 



Again, if they all combined so that the maximum electromotive force 

 is equal to the sum of them all, the hysteresis will be nearly: 



3 Dynamos and motors introduce the odd harmonics on account of the variations 

 of the self-induction of the machine, which becomes very apparent when a strong 

 current is flowing. The armature reactions may also introduce the harmonics. 



