Reactive Power Beyond Sinusoids: Scalar Selection and Information Limits

Reactive power is a fundamental concept in ac power systems and is well defined under single-frequency sinusoidal steady-state conditions. This paper revisits the complexity of defining reactive power under nonsinusoidal conditions where multiple definitions coexist, leading to different scalar values. The objective is to clarify the assumptions required for the selection of a specific scalar reactive-power measure and to quantify the information lost during this scalarization. The methodology involves analyzing contiguous finite harmonic spaces, focusing on real-bilinear, alternating scalar readouts that remain invariant under common time shifts. The study reveals that enforcing a measure to vanish for monotonic, time-invariant memoryless resistors leads to weights proportional to harmonic order. This outcome corresponds to the classical derivative measure, which is incompatible with maintaining conventional reactive power values across different harmonics. The findings highlight the specific conditions for selecting a reactive-power definition and provide an exact dimension of the remaining ambiguity in current measurements. Overall, the results contribute to a deeper understanding of reactive power in nonlinear circuits and the limitations of its scalar representations.