50 SYNCHRONOUS MOTORS 



speed diminishes, increases and the power developed also increases. 

 The condition is therefore stable for low powers. 



But the power-output is limited. Its maximum corresponds to 

 the power-line drawn tangentially to the circle. The correspond- 

 ing output, N, is the limit of possible outputs, because the effect of 

 an overload, by increasing further the lag 0, would be to bring the vector 

 OAi into a position such as OM, where the power-output would be 

 diminished, and, consequently, the motor would stop. 



The line ON, drawn through O parallel to A 2 Y, therefore defines 

 theoretically the limiting line of stability; and the limiting lag between 

 the E.M.F.'s. is equal to f. The maximum electric power applied 

 to the motor is equal to the product of the E.M.F. E 2 by the corre- 



A 2 N' 

 spending active current -=. 



t 



Likewise, on the second diagram (Fig. 27), if the excitation is sup- 

 posed to be constant and if the load is made to vary, the end of the 

 E.M.F. vector E 2 describes a circle around O as a center. Its point of 

 intersection, AQ, with the circle of zero-power (P 2 =^6), gives, theoret- 

 ically, the condition of operation without load; but, practically, the 

 power necessary to overcome friction and other losses not being equal 

 to zero, the unloaded condition will correspond to a higher point, 

 such as A"Q, situated on the power-circle P 2 =o.io P. 



When the load applied to the motor-shaft increases, the point of 

 output A 2 is displaced on its circle in the direction of increasing power- 

 outputs, i.e., toward the top, and the angle of lag 6 and the current 

 7 increase correspondingly. 



The power can increase up to the point Q 2 , where the characteristic 

 is tangent to a power-circle (Fig. 27); but it could only decrease 

 if the angle of lag were to be further increased. . The direction ON 

 therefore marks the theoretical limit of stability of operation. When 

 the angle of lag is increased further the motor falls out of step and comes 

 to a stop. 



It may be seen in the same manner that the alternator operates 

 as a generator below the point A' , and that the necessity of stability 

 of operation limits the angle of lag to the direction OM, \\hich is per- 

 pendicular to the right lines of equal power PI, and symmetrical with 

 ON, with respect to OA\. 



Maximum Power. The maximum power P 2 , corresponding to 

 the limit of stability just determined, can be easily calculated by mak- 

 ing = ?- in the general power equation (18). 



