load calculation for receptacles

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davidbananas999

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Minnesota
I was doing a practice test, and the question was figure out the load for a bunch of stuff.

A 208-volt, three-phase feeder is to supply the following loads:
Two, 5-HP three-phase induction motors,
one, 3-HP single-phase 208 induction motor,
general lighting for a 150' x 100' office area,
92, 120-volt receptacles in the office area.

I understand how to calculate everything except for the receptacles. The solution has me take the receptacle load, the larger of 220.14.K (1) or (2), which is 16,560 VA, and divide it by the voltage to find the amperage.
Their math shows 16,560 / (208 * √3)

My question is, why am I using 208 for the voltage for the receptacles when the question states they are 120 volt?

Thanks for the tips!

PS: Their answer is 276 Amps.
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davidbananas999 said:
...
A 208-volt, three-phase feeder is to supply the following loads:
Two, 5-HP three-phase induction motors,
one, 3-HP single-phase 208 induction motor,
general lighting for a 150' x 100' office area,
92, 120-volt receptacles in the office area.
...
My question is, why am I using 208 for the voltage for the receptacles when the question states they are 120 volt?
Click to expand...
You sum up the VA of the line items. Then because this is a 3 phase system, you divide by the 3 phase voltage times the square root of 3. That's just how 3 phase works... volts to balanced amps for each of the 3 line conductors.

To help you understand the principle behind it, consider (208 * √3) = 360 = (120V * 3 Lines)

PS: Their answer is 276 Amps.
Click to expand...
So what do you get? And how, if different?
 
Smart $ said:
You sum up the VA of the line items. Then because this is a 3 phase system, you divide by the 3 phase voltage times the square root of 3.
Click to expand...


Or you divide by the line to neutral voltage times 3. Which is exactly the same number. :)

Some find it easier to remember in that form.
 
I understand why I use √3 in the formula, I dont understand why it's 208 for the receptacles instead of 120 for them since they state they are 120v receps. Its not like the receptacles are connected to two legs of the panel, only 1 leg to ground.
 
davidbananas999 said:
I understand why I use √3 in the formula, I dont understand why it's 208 for the receptacles instead of 120 for them since they state they are 120v receps. Its not like the receptacles are connected to two legs of the panel, only 1 leg to ground.
Click to expand...
All the receptacles are connected to all the lines. Individually, one-third are connected to each of the three lines.

(120V * 3 Lines) = (208V * √3 three phase multiplier) = 360

You arrive at the same result no matter which way you calculate it. Convention has you do it as a three-phase equation... especially since you are calculating the minimum conductor ampacity of a three-phase feeder.
 
120V receptacle load is 16,560 VA.

One-third of the receptacles are connected to each of the three lines (hots)...

5,520 VA per line ÷ 120V = 46A on each of three lines.

16,560 ÷ (208 * √3) = 46A on each of three lines
 
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