Mathematical foundations of the instantaneous power concepts: An algebraic approach

Abstract

In this paper a mathematical framework is proposed f o r defining the concepts of instantaneous real and instantaneous imaginarypower in three-phase systems. Up to now, the approach to the definition of these quantities has mainly been a geometrical approach, which is not generally convenient f o r the quantitative analysis of the electric system behaviour: The proposed framework is an algebraic approach, based on the innovative use of the hypercomplex number algebra, which is shown to be well suited to deal with three-wire and fourwire three-phase systems. The relationship with the geometrical analysis proposed by Willems is discussed.

Load Characterization and Revenue Metering Under Non-Sinusoidal and Asymmetrical Operation

“…In this case we proceed as follows: 1) From the voltages and currents measured at PCC we estimate the parameters of the equivalent circuit of Fig.1, according to (12), (13), (14 Fig.3 we may estimate the fundamental phase currents 5) Finally, we estimate the power terms (9) accountable to the load by considering the voltages and currents at PCC occurring for ideal supply conditions:…”

“…Whatever power metering approach is taken to face such situations [11][12][13][14][15][16][17][18][19][20] it must be based on power definitions which keep their meaning even in case of distorted, asymmetrical and weak supply. This is peculiar of the Conservative Power Theory (CPT), which makes use of quantities related to power flow and energy storage, that are conservative for every network irrespective of voltage and current asymmetry and distortion [18,19].…”

Power quality indices proposal for networks operating in sinusoidal and unbalanced conditions

“…Major recent contributions are from part of LaWhite N. and M. Ilic Marija [1] about the reactive power using the vector space decomposition of the periodic non-sinusoidal signals and of Leszek Czarnecki critical approach of Budeanu's theory [2], [3.]. Notable contribution is due to A. Ferrero and L. Cristaldi related to mathematical background of instantaneous power published in 1996 [4] and to F. Peng and L. Lai who generalized the instantaneous reactive power theory for three phase circuits [5]. A recent much discussed article is that of A. Emanuel "On the Definition of Power Factor and Apparent Power in Unbalanced Poly-phase Circuits with Sinusoidal Voltage and Currents [6] or "Power Definitions and the Physical Mechanism of Power Flow", of the same author [7].…”

Synergistic control and cooperative operation of distributed harmonic and reactive compensators

“…More recently, approaches in the time domain have been devoted to the definition of instantaneous power terms, providing a background for dynamic compensation of reactive, distorting and unbalanced loads [10][11][12][13][14][15][16]. For this purpose, fast and accurate response is required, thus active power filters are employed [17][18], which may also help in damping harmonic oscillations [19].…”