A complex-vector power representation for three-phase systems supplements the classical dot-product complex power with a cross-product term to explicitly capture cross-phase unbalance, separating apparent power into intraphase and cross-phase parts while preserving norms under Fortescue transforms.
On the definition of power factor and apparent power in unbalanced polyphase circuits with sinusoidal voltage and currents
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Complex-Vector Power and Cross-Phase Unbalance in Three-Phase Systems
A complex-vector power representation for three-phase systems supplements the classical dot-product complex power with a cross-product term to explicitly capture cross-phase unbalance, separating apparent power into intraphase and cross-phase parts while preserving norms under Fortescue transforms.