THE POLYPHASE SYSTEM. Ill 



interesting consequence of this steady flow of power in a balanced 

 polyphase system is that, whereas, the driving torque of a single- 

 phase alternator must pulsate except in so far as the pulsations 

 of torque are averaged out by the fly-wheel effect of the rotating 

 armature, the driving torque of a polyphase generator is perfectly 

 steady when it delivers current to balanced receiving circuits. 

 Moreover a single-phase motor of any kind is driven by a pul- 

 sating torque, whereas a polyphase motor of any kind is driven 

 by a steady torque. 



Discussion for a two-phase alternator. Consider a single-phase alternator of 

 which the electromotive force is : 



e = E sin ut (a) 



and which gives a current : 



*=I sin (ut 6) 

 or 



i = I sin ut cos 6 I cos ut sin 6 (3) 



The instantaneous power is : 



ei = EI cos 6 sin 2 ut El sin 6 sin ut cos ut 



which pulsates with a frequency twice as great as the frequency of e and i. 



Let equations (a) and (<$) express the electromotive force and current of one phase 

 of a (balanced) two-phase alternator, then the electromotive force and current of the 

 other phase are : 



e f = E cos ut (c) 



i' I cos (ut 6)=I cos ut cos 6 -f I sin ut sin (J) 



The instantaneous power output of this phase is 



e^i' = EI cos 6 cos 2 ut -j- EI sin 6 sin ut cos ut 

 Therefore the total power output of the two-phase machine is 

 e i _|_ gfy EI cos (sin 2 ut + cos 2 ut} 



EI cos 6 

 which is constant. 



(ft) Value of power in balanced polyphase system. If A is the 

 value of the electromotive force across one of the receiving cir- 

 cuits of an rc-phase system, a the value of the current in the 

 receiving circuit, and cos the power factor, then Aa cos 6 is 

 the power delivered to the receiving circuit and the total power 

 delivered to the n similar receiving circuits is : 



P=nAacos0 (a) 



