Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply

Francisco G. Montoya, Raúl Baños, Alfredo Alcayde, Francisco Manuel Arrabal-Campos and Javier Roldán Pérez
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Francisco G. Montoya: Department of Engineering, University of Almeria, 04120 Almeria, Spain
Raúl Baños: Department of Engineering, University of Almeria, 04120 Almeria, Spain
Alfredo Alcayde: Department of Engineering, University of Almeria, 04120 Almeria, Spain
Francisco Manuel Arrabal-Campos: Department of Engineering, University of Almeria, 04120 Almeria, Spain
Javier Roldán Pérez: IMDEA Energy Institute, Electrical Systems Unit, 28935 Madrid, Spain

Mathematics, 2021, vol. 9, issue 11, 1-17

Abstract: This paper presents a new framework based on geometric algebra (GA) to solve and analyse three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an exploratory application of the geometric algebra power theory (GAPoT) to multiple-phase systems. A definition of geometric apparent power for three-phase systems, that complies with the energy conservation principle, is also introduced. Power calculations are performed in a multi-dimensional Euclidean space where cross effects between voltage and current harmonics are taken into consideration. By using the proposed framework, the current can be easily geometrically decomposed into active- and non-active components for current compensation purposes. The paper includes detailed examples in which electrical circuits are solved and the results are analysed. This work is a first step towards a more advanced polyphase proposal that can be applied to systems under real operation conditions, where unbalance and asymmetry is considered.

Keywords: geometric algebra; non-sinusoidal power; clifford algebra; power theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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