ARMATURE REACTION IN ALTERNATORS. 137 



since 



i = \/2i 



The required expression for the change of ampere turns is 

 therefore 



. - - sin 



7T 



2\/2 



iN sin < = 0-9LY sin 0, nearly . . (13) 



To find the total excitation of the field, we must add expression 

 (13) to, or subtract it from, the ampere turns on the field, accord- 

 ing as the current leads or lags in a generator, and lags or leads in 

 a motor. 



STABILITY OF A PLANT CONSISTING OF AN ALTERNATING-CURRENT 

 GENERATOR AND A SYNCHRONOUS MOTOR. 



92. The plant is said to be working in a condition of stability 

 if, for a small increase or diminution of the output of the motor, or 

 for a small increase or diminution of the E.M.F.s of generator or 

 motor, it will continue to work. 



We shall suppose the E.M.F. of the generator on open circuit 

 to remain constant, so that the question of stability will involve 

 two distinct problems. (1) Given the E.M.F.s of generator and 

 motor, and the resistance, etc., of the complete circuit consisting of 

 the two armatures and line, when will a breakdown occur if the 

 load on the motor is varied ? and (2), given the E.M.F. of the 

 generator, the output of the motor, and the resistance, etc., of the 

 complete circuit, between what limits may the counter E.M.F. of 

 the motor be varied without a breakdown occurring ? 



The fundamental equation has been obtained in the form 



= 



If E, r, S, and w are given, this equation gives a relation 

 between the current i and the counter E.M.F. e of the motor. We 

 can, therefore, plot a curve with values of e for ordinates, and cor- 

 responding values of i for abscissae ; and by giving different values 

 to w, a series of such curves will be obtained. We may call them 

 characteristic curves. A series of characteristic curves 

 is given in Fig. 46. 



