A Systematic and Comprehensive Geometric Framework for Multiphase Power Systems Analysis and Computing in Time Domain

This paper presents a new framework for a systematic and thorough generalization of the most well-known instantaneous transformations used in electrical engineering for power systems analysis and computing through geometric principles based on the language of Geometric Algebra. By introducing the concepts of Kirchhoff Vector and Kirchhoff Subspace, a new generalized transformation is presented. Thus, it is shown how the Clarke, Park or Hyper-Space vector transformations (widely used in electrical engineering) are particular cases of this unifying framework. Moreover, a generalization to an arbitrary number of phases is achieved. In order to be as close as possible to the geometrical intuition, all the underlying ideas are presented by means of spatial-like conceptualizations, substantiated by their corresponding algebraic formulation. This proposal has potential uses in a wide range of power system applications such as electrical machines, current compensation, power quality, electronic converters or transmission lines. Preliminary results show the superior efficiency of the method compared to matrix methods. Some real-world examples have been included to highlight the potential use of the method.