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Posted By: C-H Is there something wrong with my calculation? - 02/22/04 03:59 PM

I've been scratching my head over something. I have a scenario (theoretical) where you can either use 2 wires @ 230V or 3 wires @ 200V 3-ph. The size of the wires is limited by voltage drop, which is the same percentage wise for both cases. According to textbooks and common knowledge, 3-phase is more efficient than just using two wires. But I fail to arrive at this result in this case.

If I put 1A load the 3-ph case I need 1.73/1.15 = 1.5A single phase to get the same power. This means I have to increase the cross sectional area of the conductors by 50% compared to the 3-phase case. But I only need 2 wires instead of 3 and am back at the same amount of copper.

Is there something wrong with my calculations? Wouldn't be the first time... [Linked Image]
C-H, that is a great riddle/brainteaser. The “trick” is 3ø versus 1ø power must be compared at the same voltage.

1.5 amperes at 230V 1ø is 345VA, where
1 ampere at 200V 3ø is 346.4VA, BUT
1 ampere at 230V 3ø is 398.4VA.
Ratioing, 345/398.4 yields 0.866, exactly as expected.

Does that help?
Thanks! I needed to check my calculation with someone. I wanted the same potential to ground for both cases (wye or center tapped source).

By the way, are you and Busbar one and the same person?

You've found an identity [Linked Image] (In the mathematical sense.) For the same potential to neutral and the same 'aggregate current', you get the same VA delivered to the load, no matter 1 phase or 3 phase or 17 phases [Linked Image]

C-H — Yes, but only on alternate Tuesdays. ;-)
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