AUTHOREA
Log in
Sign Up
Browse Preprints
LOG IN
SIGN UP
Essential Maintenance
: All Authorea-powered sites will be offline 9am-10am EDT Tuesday 28 May
and 11pm-1am EDT Tuesday 28-Wednesday 29 May. We apologise for any inconvenience.
Francisco Montoya
Public Documents
3
Frequency Generalization via Darboux Bivector and Electrical Curves in Multi-Phase Po...
Francisco G. Montoya
and 4 more
May 19, 2023
This paper investigates the concept of frequency in arbitrary multi-phase systems based on geometrical principles. The proposed approach relies on state-of-the-art mathematical techniques such as differential geometry and geometric algebra in $\bm{n}$ dimensions. By analyzing the generalized Frénet-Serret frame, we derive how the Darboux bivector can accurately express the rotation of this frame as a rigid body in space. It is shown how the concept of frequency in power grids can be intimately linked to spatial rotations. New insights are presented based on the comparison with other recently published works. It is also concluded that the application to single-phase systems cannot always be accommodated by spatial curves. Several examples are used to illustrate the findings of this paper.
Geometric Foundations of Power Theory for Multiphase AC Systems in the Frequency Doma...
Francisco G. Montoya
and 3 more
May 11, 2023
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.
Geometric algebra framework applied to Symmetrical Balanced Three-Phase Systems for S...
Francisco Montoya
and 4 more
December 21, 2020
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.