Steady-state analysis of electrical power systems is largely based on linear and sinusoidal AC circuits which allow the concept of impedance, phasors and well-defined power quantities (i.e., real, reactive and apparent powers). In reality, however, the electric load which was once composed of linear elements (e.g., induction motors, incandescent lighting, etc …) is becoming more and more nonlinear due to the wide-spread use of electronic components such as fluorescent lighting and variable-frequency drives that power the majority of electric motors. As a consequence, the current drawn by such devices is often distorted, thus containing a number of high frequency harmonics that are superimposed on the fundamental 60 Hz component. As these high-frequency harmonic currents flow through the power distribution apparatus, they in turn cause distortion in the voltage. The distorted voltage can in turn affect other loads that share a transformer or branch circuit with the original harmonic loads.It has been shown that classical definitions of electric power; namely, active, reactive and apparent powers, do not fulfill the conditions caused by harmonics. Consequently, various power definitions and calculation methods have been proposed in the literature.It is hypothesized that existing definitions of power other than the active part in non-sinusoidal circuits are based on a non-real (i.e., frequency) domain and rate theoretical in nature. Therefore, these are not only hard (often impossible) to interpret their physical meaning and make use of them, but also hard to implement in measuring devices. On the other hand, power definitions that are based on a real time domain are expected to have simpler physical interpretations and easier to measure. A simple definition of non-active power will be of great value to the power industry. It is also hypothesized that a typical electrical power distribution system can handle significantly more non-linear loads than previously thought as modern electrical loads are less sensitive to distortion in the voltage supply.The motivation that led to the proposed works stems from the fast moving events that are taking place in the electric utility industry. more specifically, many utilities are considering additional customer charges (such as charging the residential sector for peak demand, reactive power consumption, and renewable power generation) in order to ring more profits. The recently installed smart meters that primarily record energy consumption every 5 minutes and communicate wirelessly the local utility, do have the ability to measure other electrical quantities. The way these quantities are defined and measured is of critical importance to both the supplier and consumer.
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