Maximum Active Power Transmission Efficiency and Apparent Power Definition with Arbitrary Waveforms

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A proof of the theorem giving the maximum available active power with constant transmission losses (i.e., maximum efficiency) valid for arbitrary waveforms, is proposed. This makes it possible to rigorously generalize the definitions of power factor based on the definition of apparent power as the maximum power available to apply them to systems with non-symmetric, non-sinusoidal, and eventually time-varying (i.e., non-periodic) waveforms or DC grids, thus extending its application to hybrid multi-wire systems with asymmetrical phases, with different voltages, frequencies or waveforms (i.e., non-sinusoidal waves, such as rectangular or PWM) and even DC, which can be combined eventually sharing the neutral conductor. Finally, an example of application to a hybrid system composed of DC and unbalanced load inverter-based non-sinusoidal AC subsystems is included.