Question about complex power in three phase circuits

[kstorm19]

Homework Statement

Assume that the two balanced loads are supplied by an 840-V rms 60-Hz line. Load #1: Y-connected with 30+j40 Ω per phase, Load #2: balanced three-phase motor drawing 48 kW at a power factor of 0.8 lagging. Assuming abc sequence, calculate the complex power absorbed by the combined load.

Both loads are in parallel.

Homework Equations

I= V/Z
S=VI*
S= (3)^1/2 Vl * Il

The Attempt at a Solution

I wanted to specifically know about load 1. To obtain the complex power absorbed by the combined load, I have to calculate the complex power of load 1 and load 2. Load 2 is easy, as I'm already given the power factor and the real power. I'm confused about load 1, however. If this load is in wye, and the voltage I'm being given is the line voltage, then if I divide 840/(30+j40) I will get the line current, right?

So the next thing is finding the complex power. I now have the line voltage and the current voltage, so I attempted to use the equation: S= (3)^1/2 * Line Voltage * Line Current. The result isn't correct as shown by the book answers.

So then I used the equation S=VI* and it gave me the correct answer, which is 14.112 KVA and an angle of 53.13 degrees.

My question is: why can't I use the equation S= (3)^1/2 * Line Voltage * Line Current ? Is there something that I'm missing?

Thank you very much for your time and help.

 

[magoo]

What is the line voltage? In my usage, the line voltage is the line-to-line or phase-to-phase voltage.

The phase to neutral voltage is equal to the line voltage divided by 1.732.

So, dividing a line voltage (840 in your case) by the phase to neutral impedance is not a correct expression. The phase to neutral impedance is seeing the phase to neutral voltage (i.e., 840/1.732).

 

[kstorm19]

What is the line voltage? In my usage, the line voltage is the line-to-line or phase-to-phase voltage.

The phase to neutral voltage is equal to the line voltage divided by 1.732.

So, dividing a line voltage (840 in your case) by the phase to neutral impedance is not a correct expression. The phase to neutral impedance is seeing the phase to neutral voltage (i.e., 840/1.732).

Thank you very much. I've understood now.