Ask the Engineer- How do I calculate power from 3-phase LED readings?

Question from Steven G.: How do I calculate the power usage for devices attached to one of your Smart PDUs by looking at the digital readouts on them? I understand the 3-phase power calculation of P=VA*1.73, but is that done on each leg/phase (x,y,z) for the PDU? An example from a CS-24VY-L30MA is X=4.6, Y=4.6, Z=6.3

Answer: the shortcut way to find power consumption is (X+Y+Z)*120V = 1860W for your example. This is only accurate when loads are fairly well balanced. It turns out that even though one leg is 37% higher than the other two legs, your example is balanced well enough that the power calculation is only 1.6% overestimated.

The more accurate calculation of 1831W must be found by first calculating the outlet branch amperages (XY, YZ, ZX) through an iterative process using the equations:

X = sqrt([XY]*[XY] + [ZX]*[ZX] + [XY]*[ZX])

Y = sqrt([XY]*[XY] + [YZ]*[YZ] + [XY]*[YZ])

Z = sqrt([YZ]*[YZ] + [ZX]*[ZX] + [YZ]*[ZX])

These are derived from the law of cosines with the assumption that the three legs are mutually 120 degrees apart.