CHAPTER X 



PHASE METERS, POWER FACTOR INDICATORS, SYN- 

 CHROSCOPES AND FREQUENCY METERS 



In the mathematical discussion of alternating currents, it is 

 usual to assume sinusoidal waves, in which case, 



watts 

 Power factor = cos 6 - 



volt-amperes 



where 6 is the time-phase displacement of the current wave with 

 respect to the e.m.f. wave; that is, the angular, distance between 

 the zero points of the waves. With non-sinusoidal waves the 

 power factor is taken as the ratio of the watts to the volt- 

 amperes. In this case 6 is without significance. 



The output of a generator is limited by the heating due to the 

 currents in its coils, and the financial return on this output is 

 primarily based on the true watts. For this reason alone then, 

 it is highly desirable to operate the system supplied by the 

 generator at as high a power factor as possible. Also, the power 

 factor of the load influences the voltage regulation of the system. 

 It is not unusual to employ some form of synchronous apparatus 

 as a transforming device between the generator and the load. 

 As its power factor may be controlled by varying the excitation, 

 it becomes necessary to have on the switchboard a power-factor 

 meter, or its equivalent, as an aid to the proper handling of this 

 apparatus. 



Idle Current Meters. In any reactive circuit the current will 

 either lag behind or lead the applied e.m.f. and may be resolved 

 into two components, one the power component, in time phase 

 with the voltage, the other the quadrature component which is 



WattleSS. Power Component 



* > 



Quadrature or 

 Idle Component 



FIG. 314. Showing power and quadrature components of current. 



Evidently, for sinusoidal currents, 



Power component = I cos 

 Quadrature component = J sin 0. 

 530 



