SYNCHRONOUS GENERATORS 303 



of the induced counter electro-motive force greatly differs from the 

 pressure wave acting at the terminals of a synchronous motor or 

 converter, excessive heating might result, thus lowering the 

 efficiency of the system. These results are, of course, to be 

 expected only if the distortion is considerable, and for this reason 

 it has become a general practice to limit the maximum permissible 

 deviation of the complex wave from a true sine wave to 10 per 

 cent. This deviation is to be determined by superimposing upon 

 the actual wave, as measured by an oscillograph, the equivalent 

 sine wave of equal length, in such a manner as to give the least 

 difference, and then dividing the maximum difference between 

 corresponding ordinates by the maximum value of the equivalent 

 sine wave. 



For three-phase machines the three circuits are, as previously 

 stated, connected either in star or delta. The line voltages of 

 the three phases are 120 apart and their sum must, at any instant, 

 be zero. Since the third harmonics are in phase with each other, 

 they would not add up to zero and, therefore, cannot exist, and for 

 the same reason a third harmonic of the line current cannot be 

 present. In a balanced system, third harmonics can exist only 

 in the voltage from line to neutral or Y-voltage, and in the current 

 from line to line or delta current, as will be explained in the fol- 

 lowing. 



Fig. 180 represents a delta-connected three-phase generator 

 with a predominating third harmonic e.m.f. in each phase. As 

 the three triple harmonics are in phase, the machine is really 

 running under short circuit, as far as the triple harmonic is con- 

 cerned. This triple-frequency current is internal in the windings, 

 and the e.m.f. 's which causes it to flow are short-circuited in the 

 closed delta, and will, therefore, not appear in the terminal e.m.f .'s. 

 The circulating current may be of great magnitude, entailing large 

 I 2 R losses in the windings with corresponding loss of efficiency. 



If the generator is Y-connectsd, as in Fig. 181, the terminal 

 e.m.f. between A and B is the resultant of the two e.m.f. vectors 

 OA and OB, thus OA OB, the negative sign of the latter on 

 account of its direction. The triple harmonics are the same as 

 in the previous case, but by adding the e.m.f. waves in a and 6, 

 corresponding to OA and OB, we get the resultant c. OB, that is 

 6, must, of course, be reversed and the triple harmonics will cancel 

 and no triple harmonic can, therefore, exist in the terminal e.m.f., 



