Active and Reactive Energy Balance Equations in Active and Reactive Time

Understand

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.