### Journals Information

Universal Journal of Electrical and Electronic Engineering Vol. 6(3), pp. 101 - 107
DOI: 10.13189/ujeee.2019.060303
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## Linear Algebra Based Generalization of the Kennelly's Theorem

Ali Krim *, Abderrazak Lakrim , Driss Tahri
Electrical Department, Faculty of Sciences and Technologies, Sidi Mohamed Ben Abdellah University, Morocco

ABSTRACT

The Kennelly theorem which is widely used in three phase systems allows for the delta-star and star-delta conversion and simplification of several electronic circuits. In the present work, we propose a generalization based on the theorem of superposition and some results of linear algebra. Our demonstration is inspired from the proof of the classical Kennelly's theorem. The proposed formulas are very clear and simple. This will make it possible to convert polygon-start and star -polygon if the number of impedances is odd, greater than or equals three. The advantage of our proposal is that it could be understood and programmed easily by undergraduate student when compared to other methods based on the graph theory, which focuses mainly on the mesh-star conversion, which is not possible in all configurations in both ways. This result can be applied to reduce the number of nodes in circuit type models of electrical components and electronic circuits. Thus, the simulation time is reduced.

KEYWORDS
Delta-star Transformation, Polygon-star Transformation, Distribution Network, Circuit Theory

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ali Krim , Abderrazak Lakrim , Driss Tahri , "Linear Algebra Based Generalization of the Kennelly's Theorem," Universal Journal of Electrical and Electronic Engineering, Vol. 6, No. 3, pp. 101 - 107, 2019. DOI: 10.13189/ujeee.2019.060303.

(b). APA Format:
Ali Krim , Abderrazak Lakrim , Driss Tahri (2019). Linear Algebra Based Generalization of the Kennelly's Theorem. Universal Journal of Electrical and Electronic Engineering, 6(3), 101 - 107. DOI: 10.13189/ujeee.2019.060303.