Why is using a single phase device across phases of a 3 phase outlet OK?

Question

My friend connected two wires to two "non-earth hole" in a 3 phase outlet (208V) to run a 220V single phase blower (Note: the outlet has four holes, one of them is earth). Basically, he used the potential difference of those two holes. I don't know why it is OK, so I used MATLAB to draw 4 curves (See picture)

Blue - regular sine wave 208V (peak is 208*sqrt(3)) where sqrt(3) is three phase peak ratio

Red - Same as Blue but with 2/3 pi shift

Green - The difference between Blue and Red

Black - regular sine wave 220V (peak is 220*sqrt(2)) where sqrt(2) is single phase peak ratio

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Officially, the green peak is >1.73 times the blue one. If the blower uses 220V single phase AC, then the blower should be connected to

----calculation process-----

Peak voltage of 220V AC = average voltage*single phase peak ratio = 220V*1.41 = 310.2V

Peak voltage of two legs out of three phase = (two legs potential difference from diagram)average voltagethree phase peak ratio = 1.73*average voltage*1.73 = 3*average three phase voltage

310.2/3 = 103.4V

-----end of calculation process----------

103.4V three phases power outlet (Two holes of a 3 phase outlet). Note: I understand that there is no such 103.4V three phase power outlet.

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Am I right?

Answer 1

Any cross phase wiring of a WYE connection will yield sqrt(3)* higher voltage. You have shown this in your simulation. This can also be determined via phasor analysis.

The current flow in these phases will no longer be balanced, which may or may not be a concern.

As you note the motor will be running at 208V instead of it's designed 220 (which BTW is actually 110 @ 0degrees and 110 at 180 degrees). This motor is designed to take two active phases so insulation issues should be safe.

Yes, you are right.