Mathematical foundations of the instantaneous power concepts: an algebraic approach

In this paper a mathematical framework is proposed for defining the concepts of instantaneous real and instantaneous imaginary power 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 for the quantitative analysis of the elctric 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 four-wire three-phase systems. The relationship with the geometrical analysis proposed by Willems is discussed.