The general non-symmetric, unbalanced star circuit: On the geometrization of problems in electrical measurement

TL;DR

This paper transforms complex AC star circuit problems into geometric problems, revealing connections to the Fermat point and providing practical solutions for non-symmetric, unbalanced circuits.

Contribution

It introduces a geometric approach to analyze AC star circuits, including a generalization for unbalanced configurations, offering new insights and practical solutions.

Findings

Connection between AC star circuits and Fermat point geometry

Generalized geometric solution for unbalanced circuits

Practical application-oriented problem-solving method

Abstract

We provide the general solution of problems concerning AC star circuits by turning them into geometric problems. We show that one problem is strongly related to the Fermat-point of a triangle. We present a solution that is well adapted to the practical application the problem is based on. Furthermore, we solve a generalization of the geometric situation and discuss the relation to non-symmetric, unbalanced AC star circuits.