CHAPTER VIII 



GENERALIZATION OF DIAGRAM FOR COUPLED 

 SYNCHRONOUS MACHINES 



THE diagram represented in Fig. 27 (page 44), which is based 

 upon Joubert's theory that the armature-reaction of the alternator 

 employed can be adequately explained by supposing the presence 

 in the armature of a simple mean synchronous reactance, can be 

 retained to advantage for certain purposes even in the case of the 

 theory of " two reactions," developed by the author in Part III, 

 Chapter I, for alternators with saturated magnetic fields. It 

 may, indeed, be noted that the impedance Z, which enters into the 



expression for the vector, AiAz, is still a constant of the same char- 

 acter as before, though it now represents the impedance of the trans- 

 verse reaction, which may be symbolized by Z, when we take 



We will first suppose the case of two alternators which comply 

 with Joubert's law (i.e., which have a constant synchronous react- 

 ance). The clearest form of electrical transmission diagram will be 

 obtained by first combining the diagrams shown in Fig. 27 (page 44) 

 and in Fig. 43 (page 86). All that is necessary is to point off along OA 

 (Fig. 84) a distance proportional to the voltage (7) at the terminals 

 of the two alternators, these being assumed to be near each other. 

 (If they are far apart the impedance of each one is to be increased 

 fictitiously by an amount equal to half the impedance of the line 

 by which they are coupled together). The vectors of the e.m.f.'s 

 of these alternators are then drawn in proper magnitude and phase. 

 (The alternators may be unlike provided they both have the same 



characteristic ratio =tan y)- We then draw the line of zero 



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