82 



ALTERNATING CURRENTS 



Power in Y-system. Figure 80 shows the three currents 7 oa , 

 lob and I oc of coils oa, 06, and oc respectively. Unity power-factor 

 is assumed and the three currents are therefore in phase with 

 their respective coil voltages. A balanced system is assumed 

 and the three currents are therefore equal in magnitude. 



The coil current I oa and the line current I aa ' are the same 

 current. Therefore, the line current I aa > is 30 out of phase with 

 the line voltage E ca , when the power-factor is unity. This is 

 true for each phase. 



The power delivered by each coil is 



P' = E oa I oa (unity power-factor) 

 and the total power delivered by the generator is three times this. 



P = S 



FIG. 80. Relation of line to coil volt- FIG. 81. Relation of line to coil 

 ages and currents in a Y-system, unity voltages and currents in a Y-system. 

 power-factor. Power-factor =cos 6. 



As the power in the line is the same as that delivered by the 

 generator, substituting En re /\/3 for the value of E co u, 



o 

 P = ~/K Eline Icoil = \/&Eum* Iline (29) 



the coil current and the line current being equal. 



In a balanced three-phase system, the line power at unity power- 

 factor is equal to \/3 times the line voltage times the line current. 



Figure 81 shows this same three-phase system when the power- 

 factor is no longer unity. Each coil current now lags its respec- 

 tive coil voltage by the angle 6. 



