Power factor and x/r ratio...

[whycliffrussell]

Am I correct in saying (for a 3 phase I/M):

pf=cos(atan(x/r)) ?

I am using this to calculate pf for motors based on x/r ratios provided in ieee std. 141-1976 (ieee red book)...pp202 fig. 79) and am getting pf results that are very low (too low to seem realistic)

Is there an err. in my reasoning or understanding of this table and it's values?

 

[jghrist]

Your equation is correct, but the X/R ratios in the red book (Fig. 4A-3 in IEEE Std 141-1993) are for fault conditions, not load conditions. The power factor of induction motors depends on the load. IEEE Std 141-1993 Fig. 8-11 shows typical motor characteristics and Table 8-1 gives typical power factor values by industry and operation.