280 ELEMENTS OF ELECTRICAL ENGINEERING. 



resistance R" per stator phase is defined in any case by the rela- 

 tion : Actual rotor RP losses = qR n 'I' 2 , in which q is the 

 number of stator phases and /' is the load current per phase in 

 the stator. 



The value of R" may be calculated from the measured cur- 

 rent and power input per stator phase at standstill as follows, R' 

 having been measured. The core loss per phase at zero load 

 equals OM^ x E f minus R' x OM . The core loss is assumed 

 to be the same at all loads. The measured power input per 

 phase at stand-still minus the core loss per phase minus 

 R f x OP 2 (see Fig. 242) is equal to the rotor RP loss per 

 phase at stand-still, and this is equal to R" I' 2 where /' is the 

 current represented by MP '. 



Use of circle diagram for calculating the performance cumes 

 of an induction motor. Having determined the values of 

 R' and R", the performance curves of the induction motor 

 may be determined from the circle diagram as follows : Take 

 a series of positions of the point P on the circular current 

 locus, and for each position make the following calculations : 

 Motor intake equals OQ X E f x q where q is the number of 

 phases. Power factor of motor equals the cosine of the angle 

 POE'. The power a delivered to the rotor equals OQxE'xq 

 minus core loss per phase x q minus R' x OP 2 . Electrical power 

 b developed in rotor equals R" x MP* x q. Mechanical power 

 developed in rotor equals difference between a and b. Motor 

 slip may be found from the relation b = sa, and motor speed ;/' 

 is then known since synchronous speed n is known. Efficiency 

 equals a b divided by total motor intake. Torque may be 

 found from the relation 2 r irnT a ; this gives the value of the 

 torque in watts per unit angulai velocity, that is in watts per 

 radians per second. The value of torque may be most conveni- 

 ently expressed in terms of the power a directly, which is the 

 power in watts that the actual torque would develop if it were to 

 drive the rotor at synchronous speed, that is to say, the value of 

 a expresses torque in " synchronous watts " so called. 



