/A'NVAT VA.V7 7 TRANSFORMERS 57fl 



It has just been shown that the power in a single-phase circuit 

 is given by 



Assume thai the t ransformer ratios are 1:1, then in the two- 

 watt meter method the power which should be indicated by the 



two instruments is 



/', VI cos (30 + 0). 

 !> 17 C og ;;o - 0). 



So 



= V/[co^ 30 f 9) + cos (30 - 0)] =F/\/3 cos 0. 



The etVect of the phase angles of the transformers and that of 

 the |>ofential circuit of the wattmeter is to reduce the phase dif- 

 ference of the currents in the fixed and movable coils of the watt- 

 meters by the angle + 0,. - 7; the readings become: 

 (Heading)! = VI cos [30 + - - B P + 7] = VI cos [30 + 0']. 

 (Hcading) 3 = VI cos [30 - 6 -f ft + B P - 7] = VI cos [30 - 0']. 

 (Heading of meters) == F/\/3 cos 0'. 



BoP = (Readin. 



>y cos 



That is, the fractional error due to the phase angles is tho same 

 as that occurring in a single-phase measurement at the same 

 power factor. 



If the load is not balanced the readings of each instrument 

 should be corrected as in a single-phase measurement. 



Use of Transformers with Watt -hour Meters. It is customary 

 t<> use instrument transformers in connection with induction 

 watt-hour meters. In this case, especially at low power factors, 

 an additional complication is introduced, for both the phase 

 angles of the transformers and the adjustments of the phase 

 K-la tions of the fluxes in the potential circuits of the meters 

 affect the measurements. 



To be ideally perfect an induction meter, when used with a 

 current t?-ansformer, would have to be lagged so that the time- 

 phase angle between the potential coil flux and the current in 

 tin- secondary of the current transformer plus the power-factor 

 Mngle of the load would be 90. This suggests that the watt- 

 hour meter and the transformers be treated as a unit when the 



