Active and Reactive Energy Balance Equations in Active and Reactive Time

TL;DR

This paper introduces a novel framework for defining and analyzing reactive energy and power in electrical networks using the concept of reactive time, extending the classical energy balance to non-sinusoidal waveforms.

Contribution

It specializes the reactive time concept to RLC networks, providing a physically motivated way to generalize reactive power beyond sinusoidal conditions.

Findings

Reactive energy rate of change in reactive time aligns with traditional reactive power.

The approach applies to non-sinusoidal waveforms, capturing essential reactive energy properties.

Provides a resolution to the debate on reactive power generalization.

Abstract

Electrical networks, and physical systems in general, are known to satisfy a power balance equation which states that the rate of change of the energy in time equals the power at the port of the network minus the power dissipated. However, when complex power is considered, there does not seem to exist a similar statement for the imaginary power, either in the time-domain or the frequency-domain. Recently, in the context of electromagnetic fields, it has been shown by complexifying the time to t+js and interpreting s as reactive time, that it is possible to set up an imaginary power balance in terms of the rate of change of reactive energy in reactive time. Here these ideas are specialized to linear and time-invariant RLC networks. For non-sinusoidal waveforms it is shown that the rate of change of reactive energy in reactive time contains all the essential properties and features of the commonly accepted definition of reactive power under sinusoidal conditions. We believe that this provides an unambiguous and physically motivated resolution to the longstanding debate on how to generalize reactive power to non-sinusoidal waveforms.