62 SYNCHRONOUS MOTORS 



For the particular case ^2=0, this equation reduces to 



which represents one of the ellipses of zero-load already determined. 

 The reactive current /, with respect to E\, is obtained by writing the 

 relation between E 2 and E\, as it is depicted in Fig. 26, thus 



E 2 2 =E 1 2 + (Z/)2- 2 EiZ(* cos r +j sin r ), 

 or 



+ . 2 _ 2E R 



V J \ Eg 



With no load, when P 2 =o, this equation reduces to 



The curve of / as a function of E 2 , drawn in rectangular co-ordinates, 

 would therefore be a hyperbola; we can write 



z 



The horizontal axis is situated at a distance 



X 2 \ 

 -\ 



z 2 )' 



Z 2 ' 



above the axis of volts. 



These formulae enable the reactive currents to be calculated alge- 

 braically with more precision, but also much more laboriously, than 

 by the graphical method. 



Comparison of Outputs which the Same Alternator Can Develop 

 with the Same Terminal Voltage, when Used Either as a Generator 

 or as a Motor. Two different cases have to be considered: 



(i) Let us suppose the case of an alternator connected to a con- 

 stant potential system of great power, presenting a negligible impedance, 

 and let the excitation be regulated in such a manner as to give the 

 minimum current. Assuming a sufficient margin for regulating the 

 excitation, the output of the machine will be limited in all practical 

 cases by the value of the armature-current. 



