Instantaneous Reactive Power Theory in the Geometric Algebra Framework

Abstract

In this paper, a new approach for instantaneous reactive power analysis in the geometric algebra (GA) environment is presented. The different formulations of the instantaneous reactive power theory (IRPT) proposed, to date, have been developed in three-phase systems. There, an instantaneous power variable, and two/three reactive power variables, all handled independently, were introduced. Thanks to GA, it is possible to carry out a global treatment where an instantaneous power multivector is defined. Thus, in the same multidimensional entity all the power variables are included. From the instantaneous power multivector, the instantaneous power current and the instantaneous reactive current are determined. It should be noted that in this mathematical framework there is no limitation on the number of phases, and the extension of the IRPT to the analysis of multi-phase systems appears in a natural manner. In this study, a systematic approach with the most relevant definitions and theorems corresponding to the proposed methodology has been established. Two practical cases of five-phase and three-phase systems have been included to apply the new established formulation.

Application of a Multidimensional Approach in the Compensation of Industrial Loads

“…The IRPT formulation was first addressed in the GA framework in [28], and later, in a regular journal [29], the issue was formalized mathematically. An application of the proposed formulation for compensation using a series of hybrid active filters can be found in [30].…”

“…An application of the proposed formulation for compensation using a series of hybrid active filters can be found in [30]. In these works, [28][29], the formulation was subordinated from its origin to an orthogonal coordinate system, and there was no identification with the formulations established up to that moment. Similarly, its application from an experimental perspective has not been accredited.…”