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

Montoya, Francisco G.; Alcayde, Alfredo; Arrabal-Campos, Francisco M.; Pérez, Javier Roldán

doi:10.3390/math9111259

Cited by 8 publications

(6 citation statements)

References 31 publications

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“…Note that other approaches exist for defining the PV, such as those based on the use of space-time tensors and Noether's theorem 21 . However, they are not the most suitable and adequate for working with electrical circuits, thus the use of GA is preferred instead due to its greater simplicity and convenience in the field of electrical engineering as it has been shown in recent works [22][23][24] .…”

Section: D Spatial Power Flow and Poynting Vector In The Geometric Al...mentioning

confidence: 99%

New mathematical model based on geometric algebra for physical power flow in theoretical two-dimensional multi-phase power circuits

Montoya

Prado

Arrabal-Campos

et al. 2023

Sci Rep

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This study proposes an explanation for the physical power flow in planar circuits by analogy to theoretical two-dimensional circuits using a new mathematical model based on Geometric Algebra (GA) and 2D Maxwell’s equations. In contrast with traditional 3D physics in the observable real world, the magnetic field can be defined as a bivector instead of an axial vector allowing to obtain the Poynting Vector directly in a 2D flat world, where physical variables of planar circuits can be obtained. This approach is presented here for the first time to the best of the author’s knowledge. Previous investigations have focused on simplifications and symmetries of real 3D circuits studied mainly in the phasor and frequency domain. In this work, the electromagnetic power flow phenomenon is analyzed on a completely 2D time-domain basis and derived directly from the undisputed Maxwell equations, formulated in two dimensions. Several cases of special interest in AC multi-phase circuits are presented using the proposed technique, bringing a new simplified approach to the measurement of power flow exchange between the source and the load. It suggests a new way to understand energy propagation from a purely physical point of view.

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Section: D Spatial Power Flow and Poynting Vector In The Geometric Al...mentioning

confidence: 99%

New mathematical model based on geometric algebra for physical power flow in theoretical two-dimensional multi-phase power circuits

Montoya

Prado

Arrabal-Campos

et al. 2023

Sci Rep

Self Cite

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“…This work extends and elaborates on the results of [23] and [24] by presenting the theoretical framework in multi-phase electrical systems using symmetrical components. Specifically, three-phase circuits are thoroughly analyzed in detail.…”

Section: Contributionmentioning

confidence: 76%

Geometric Foundations of Power Theory for Multiphase AC Systems in the Frequency Domain

Montoya¹,

Ventura²,

Arrabal-Campos³

et al. 2023

Preprint

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<p>This research paper presents a new approach to power definitions in multiphase AC systems in the frequency domain from a purely geometric approach. The theoretical foundation is based on Geometric Algebra (GA) framework, which enables the representation of harmonic voltages and currents as multidimensional vectors in Euclidean space. The use of the geometric product allows to compute the geometric power multivector. The proposed method is a generalization and extension of previous works that have focused on single- phase and balanced three-phase systems. This paper introduces a complete analysis of new power terms in arbitrary multi- phase electrical systems entirely rooted on Geometric Algebra and Symmetrical Components. Several synthetic and real-world examples are presented to illustrate the novelty, effectiveness and accuracy of the proposed approach. The results of this study contribute to the development of a new geometric foundation for the power theory in electrical engineering. </p>

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“…With this knowledge at hand, it is clear that major upgrades to existing power theories based on GA appear 38 and instantaneous power, 39 apparent power, 40 power flow, 41 and non‐active power 42 calculations are formulated in GA terms for non‐sinusoidal circuits. Montoya et al 43 analyze three‐phase balanced electrical circuits under sinusoidal and non‐sinusoidal voltage supply.…”

Section: Engineering Applicationsmentioning

confidence: 99%

Current survey of Clifford geometric algebra applications

Hitzer

Hildenbrand

2022

Math Methods in App Sciences

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

Cited by 8 publications

References 31 publications

New mathematical model based on geometric algebra for physical power flow in theoretical two-dimensional multi-phase power circuits

New mathematical model based on geometric algebra for physical power flow in theoretical two-dimensional multi-phase power circuits

Geometric Foundations of Power Theory for Multiphase AC Systems in the Frequency Domain

Current survey of Clifford geometric algebra applications

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