Question 16.18: The load in Figure 16–23 is Y-connected with a phase impedan......
The load in Figure 16–23 is Y-connected with a phase impedance of Z_{Y} = 12 + j5 Ω/phase and the line voltage at the load is V_{L} = 440 V (rms). Find the line current I_{L} and the complex power delivered to the load.
Since V_{L} = 440 V(rms), the phase voltage at the load is V_{P} = 440/\sqrt{3} = 254 V (rms). In a Y-connected load, this voltage appears across the phase impedance Z_{Y} and the line current is found to be
I_{L} = \frac{V_{P}}{|Z_{Y}|}= \frac{254}{|12 + j5|}= 19.5 A (rms)
The scalar I_{L} is the rms current in all three phase impedances Z_{Y}. Hence, the total complex power delivered to the load is
S_{L} = 3I^2_{L}Z_{Y} = 3(19.5)^2 (12 + j5)
= 13.7 × 10³ + j5.73 × 10³ VA
No phasors were needed to solve this problem. The power flow in a balanced three-phase circuit can usually be found using only the scalars V_{L} and I_{L} together with the line and load impedances.