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Electrical networks, and physical systems in general, are known to satisfy apower balance equation which states that the rate of change of the energy intime 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 asimilar statement for the imaginary power, either in the time-domain or thefrequency-domain. Recently, in the context of electromagnetic fields, it hasbeen shown by complexifying the time to t+js and interpreting s as reactivetime, that it is possible to set up an imaginary power balance in terms of therate of change of reactive energy in reactive time. Here these ideas arespecialized to linear and time-invariant RLC networks. For non-sinusoidalwaveforms it is shown that the rate of change of reactive energy in reactivetime contains all the essential properties and features of the commonlyaccepted definition of reactive power under sinusoidal conditions. We believethat this provides an unambiguous and physically motivated resolution to thelongstanding debate on how to generalize reactive power to non-sinusoidalwaveforms.

Active and Reactive Energy Balance Equations in Active and Reactive Time