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I am confused about how the power factor is defined for an unbalanced 3-phase load?

Wouldn't it make much more sense to ask for a particular phase of the unbalanced 3-phase load?

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What would make the most sense would be to determine the power factor for each phase of an unbalanced 3-phase load. You could define the power factor as the average power divided by the average volt-amperes, but I don't know what you would use the information for. When an unbalanced load is found you might be concerned about how to get it balanced. Another concern would be to make sure the highest phase current is within capacity limits.

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