Note on star-triangle equivalence in conducting networks

TL;DR

This paper revisits the star-triangle equivalence in conducting networks using discrete Poisson equations, explicitly restating Kennelly's transformation formulae to clarify their application.

Contribution

It provides a clear derivation of Kennelly's star-triangle transformation using discrete Poisson equations, enhancing understanding of network equivalence.

Findings

Explicit restatement of Kennelly's transformation formulae

Derivation using discrete Poisson equations

Clarification of star-triangle equivalence

Abstract

By using the discrete Poisson equations the star-triangle (external) equivalence in conducting networks is considered and the Kennelly famous transformation formulae [Kennelly A E 1899 Electrical World and Engineer 34, 413] are explicitly restated.