Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform

Mathematics

Francisco M. Arrabal-Campos¹  Raúl Baños¹  Francisco G. Montoya¹  Alfredo Alcayde¹  Javier Roldán-Pérez² 

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

关键词: geometric algebra;    non-sinusoidal power;    Clifford algebra;    power theory;    geometric electricity;   

DOI  :  10.3390/math10091419

来源: DOAJ

【 摘 要 】

In this paper, power flows in electrical circuits are modelled in a mixed time-frequency domain by using geometric algebra and the Hilbert transform for the first time. The use of this mathematical framework overcomes some of the limitations of some of the existing methodologies, in which the so-called “active current” may not lead to the lowest Root Mean Square (RMS) current under distorted supply or unbalanced load. Moreover, this current may contain higher levels of harmonic distortion compared to the supply voltage. The proposed method can be used for sinusoidal and non-sinusoidal power supplies, non-linear loads and single- and multi-phase electrical circuits, and it provides meaningful engineering results with a compact formulation. It can also serve as an advanced tool for developing algorithms in the power electronics field. Several examples have been included to verify the validity of the proposed theory.

【 授权许可】

Unknown