A Generalized Theory of Power

TL;DR

This paper introduces a unified complex power theory that clarifies the power triangle, decomposes power into active and reactive components, and applies to both sinusoidal and non-sinusoidal waveforms with spectral analysis.

Contribution

It presents a generalized complex power representation that unifies active and reactive power, applicable to various waveform types and supported by spectral analysis and hardware diagrams.

Findings

Power triangle can be represented as a rotating phasor.

Active and reactive power are encoded in in-phase and quadrature components.

Spectral analysis confirms consistent behavior across frequencies.

Abstract

The complex representation of real-valued instantaneous power may be written as the sum of two complex powers, one Hermitian and the other non-Hermitian, or complementary. A virtue of this representation is that it consists of a power triangle rotating around a fixed phasor, thus clarifying what should be meant by the power triangle. The in-phase and quadrature components of complementary power encode for active and non-active power. When instantaneous power is defined for a Thevenin equivalent circuit, these are time-varying real and reactive power components. These claims hold for sinusoidal voltage and current, and for non-sinusoidal voltage and current. Spectral representations of Hermitian, complementary, and instantaneous power show that, frequency-by-frequency, these powers behave exactly as they behave in the single frequency sinusoidal case. Simple hardware diagrams show how instantaneous active and non-active power may be extracted from metered voltage and current, even in certain non-sinusoidal cases.