This paper rigorously considers the concept of apparent power in unbalanced three-phase situations. The analysis shows that there are various related but different concepts that can be associated with the apparent power. In particular two approaches are covered, the one relating to the literature on the single-phase sinusoidal case, the other relating to the recent IEEE Standard 1459-2000. The underlying ideas for each concept are given; the relationship and the differences between them are thoroughly discussed.
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Willems et al. (2005) studied this question.
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