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Geometric algebra framework applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply
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  • Francisco Montoya,
  • Raul Baños,
  • Alfredo Alcayde,
  • Francisco M. Arrabal-Campos,
  • Javier Roldan-Perez
Francisco Montoya
Universidad de Almeria
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Raul Baños
Universidad de Almeria
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Alfredo Alcayde
Universidad de Almeria
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Francisco M. Arrabal-Campos
Universidad de Almeria
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Javier Roldan-Perez
IMDEA - Energy
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Abstract

This paper presents a new framework based on geometric algebra (GA) for solving and analysing three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an application of the geometric algebra power theory (GAPoT) to three-phase systems. Calculations are performed in a multi-dimensional Euclidean space where cross effects between voltage and current harmonics are taken into consideration. A definition of geometric apparent power for three-phase systems that complies with the energy conservation theorem is introduced. By using the proposed framework, the current can be easily 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 with realistic cases, where unbalance and asymmetry is included.