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

Mathematics

Raúl Baños¹  FranciscoG. Montoya¹  FranciscoManuel Arrabal-Campos¹  Alfredo Alcayde¹  Javier Roldán Pérez² 

[1] Department of Engineering, University of Almeria, 04120 Almeria, Spain;IMDEA Energy Institute, Electrical Systems Unit, 28935 Madrid, Spain;

关键词: geometric algebra;    non-sinusoidal power;    clifford algebra;    power theory;   

DOI  :  10.3390/math9111259

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown