Analyze the balanced circuit shown in Figure 5.11 assuming that the transformer
ID: 2080032 • Letter: A
Question
Analyze the balanced circuit shown in Figure 5.11 assuming that the transformer ratio of every single-phase transformer is Squareroot 3:1 (that is, the 208 V, winding is the ratio of primary and the 120 V winding is the secondary). Vs = 120 V W1 = 70 W(W1 & W2 are the lectures of the two-wattmeter set, check appendix A) W2 = 150 W PF = 0.85 Find the line and phase currents in both primary and secondary sides of the transformer bank if Vs = 120 V Calculate the line voltages at both primary and secondary sides of the transformer bank. Calculate the phase load voltage. Calculate the three-power source real, apparent and reactive power delivered by the power source. Determine the power consumption of each load. What is the ratio if the line-to-line voltage at the load side to that at the source? Find the phase impedance.Explanation / Answer
The system is connected to two wattmeter method and hence taking that into consideration lets start to slove the problem(in absence of apendix A):
For solving each part lets first calculate all the required datas
Now, input voltage(Vs)= 120V, this is the phase voltage of each phase of generator which is in star connection
Two wattmeter of having load of 70W and 150W are connected before load having pf of 0.85.
this makes the total load to be supplied by the transformer is P=VIcos = (P1+P2)cos = (70+150)*0.85= 187Watt
thus we come into conclusion that the total load on the system is 187 Watt
now line current on primary side of transformer is I=P/Vcos =187/120*0.85= 1.833 A
and by taking into consideration turns ratio of 3:1 = Isec/Ipri = (3/1)/ Ipri = Isec = 1.833/1.732 = 1.06 A
Now primary side of transformer is delta and the line voltage fed to it is 120V, so the line and phase voltage is 120V for pimary side of the transformer
for secoundary side the volatge ratio is 3:1 so line voltage on secoundary side is = 120 = 360V
thus phase voltage on secoundary side will be =3 X 360 = 623.53 V
Real power of phase will be P=VxI = 360X1.06 = 381.6 VA
Active power = V X I X Cos = 360 X 1.06 X 0.85 = 324.36 Watt
Reactive power= V X I X sin = 360 X 1.06 X 0.53= 202.248 VAr