Instantaneous Reactive Power Theory in the Geometric Algebra Framework

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.

Automated summary

This paper presents a new approach for instantaneous reactive power analysis using geometric algebra (GA). Previous formulations of the instantaneous reactive power theory (IRPT) were developed for three-phase systems, where instantaneous power and reactive power variables were handled independently. With GA, a global treatment is possible by defining an instantaneous power multivector that includes all power variables within the same multidimensional entity. From this multivector, the instantaneous power current and the instantaneous reactive current can be determined. The advantage of this mathematical framework is the ability to analyze multi-phase systems without limitations. The proposed methodology is demonstrated through practical cases of five-phase and three-phase systems.