Amps Are All Askew

Dear Swami,

I'm stumped (and so is everyone I've asked thus far). I can't seem to figure out the power draw on a show. Here's the layout:
15 - VL4k spots @ 208V; 16,000W each = 24,000W

3 - Clay Paky Alpha 800 @ 208V;  1200VA each =  3600W (assuming PF = 1)

12 - S4 Series 2 Lustr @ 208V; 168W each =  2016W

3 - Colorado Solo1 @ 208V; 62W each =  186W

So that's:

24,000
  3,600
  2,016
     186
29,802W total  
The incoming voltage from the service is about 117V phase-to-neutral and about 202V phase-to-phase. When I do the math (29,802W ÷ 202V), I keep coming up with 147.5A total, or 49 amps per leg in a balanced 3-phase system. What my meter is telling me is about 82 to 86 amps with every light in the rig on full. Unfortunately, audio and video are using the same service, so that pushes it up to the low 90s range, and it's a 100-amp service, so it is way too close.

Am I missing some basic part of these power calculations? Why are my calculations missing the mark?

Signed,
Miss Calculation


Dear Miss C,

The Swami loves problems like this. The more confounding, the better. But in this case, I think it’s a simple case of using the wrong formula. You’re applying the single-phase power formula to a 3-phase system, which will give you the wrong result. 

The 3-phase power formula is P = V x I x PF x 1.732. If you have a total of 29,802 watts at 202V, then the current I = 29,802 ÷ (202 x PF x 1.732). If the PF for all of this gear is 1, or very close to it, then I would be 85 amps per leg or about 255 total amps. It turns out that the power factor of the S4s is about 0.9, so that will add a little bit of current as well. When when you add the audio load, that is what is pushing it into the 90 amp range. 

You could use the single-phase power formula and arrive at the same answer, provided you use the right voltage for the formula. The key is to use the phase-to-neutral voltage if you're going to use the single-phase formula or the phase-to-phase voltage if you're going to use the 3-phase formula. In this case, 29,802 watts divided by 117 volts (which is the phase-to-neutral voltage), you'll get 255 total amps.

Be well.
Swami Candela of the Third Millennium

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