DESIGN OF ALTERNATORS 



247 



same as that of the e.m.f. developed in the armature windings. 

 Thus, what is known as the third harmonic, and all multiples 

 of the third harmonic, are absent from the voltage measured 

 across the terminals of a star-connected three-phase generator. 

 By the third harmonic is meant a sine wave of three times the 

 periodicity of the fundamental sine wave, which, when superim- 

 posed on this fundamental wave, produces distortion of the 

 wave shape. 



A voltmeter placed across the terminals of a star-connected 

 generator measures the sum of two vector quantities with a 

 phase difference of 60 degrees (see Fig. 94). Since a phase dis- 

 placement of 60 degrees of the fundamental wave is equivalent 

 to a phase displacement of 60 X 3 180 degrees of the third 

 harmonic, it follows that the third harmonics cancel out so far 

 as their effect on the terminal voltage is concerned. The general 

 rule is that the nth harmonic and its multiples cannot appear 

 in the terminal voltage of a star-connected polyphase generator 

 of n phases. The same arguments apply to the line current of a 

 mes/i-connected polyphase generator; the nth harmonic of the 

 current wave can circulate only in the armature windings; it 

 cannot make its appearance in the current leaving the terminals 

 of the machine. 



72. Power Output of Three-phase Generator. Let E and / 

 be the line voltage and line current, and let E a and I a stand for 

 the phase voltage and armature current, respectively; then, in 

 the A-connected machine, 



E = E a 

 and 



I = V3I. 



while, in the Y-connected machine, 



E = V%E a 

 and 



I = la 



Assuming unity power factor, we may write: 

 Output of A-connected machine = 3(E a I a ) 



and, similarly, 



