The generalization of A. E. Kennelly theory of complex representation of the electrical quantities in sinusoidal periodic regime to the one and three-phase electric quantities in non-sinusoidal periodic regime

TL;DR

This paper introduces a new mathematical approach using complex linear operators to extend the representation of electrical quantities from sinusoidal to non-sinusoidal periodic regimes, enhancing analysis capabilities.

Contribution

It presents a novel mathematical method that generalizes A. E. Kennelly's complex representation theory to non-sinusoidal periodic electrical quantities.

Findings

New mathematical method based on complex linear operators.

Generalization of complex representation theory to non-sinusoidal regimes.

Enhanced analysis of electrical circuits in non-sinusoidal conditions.

Abstract

In this paper, a new mathematical method of electrical circuits calculus is proposed based on the theory of the complex linear operators in matrix form. The newly proposed method generalizes the theory of complex representation of electrical quantities in sinusoidal periodic regime to the non-sinusoidal periodic regime.