The Ohm’s Law for (non-symmetric) three-phase three-wire electrical circuits: From a complex-valued to a geometric algebra approach

A. Dòria-Cerezo, M. Velasco, I. Zaplana and P. Martí

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PB, 473-488

Abstract: This paper introduces the modelling of three-phase electrical systems using the Geometric Algebra approach and is compared with the complex-valued framework in the case of non-symmetrical conditions. The main benefit of the geometric algebra framework is the possibility of representing the dynamics of unbalanced scenarios by a single-input, single-output relationship. The paper presents step-by-step, building the geometric impedance and revisiting Ohm’s law, and compares the complex-valued modelling widely used in balanced three-phase circuits.

Keywords: Three-phase electrical circuits; Ohm’s law; Hypercomplex algebra (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pb:p:473-488

DOI: 10.1016/j.matcom.2025.10.010

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