Mathematical Derivation of the Inductance Matrix for Generic Three-Phase Transmission Lines Based on Electromagnetic Principles

Abstract

Inductance is a highly significant parameter in the study and design of power transmission lines, directly influencing the performance of power electrical systems in both steady-state and transient conditions. This work aims to formulate generalized mathematical expressions for the calculation of inductance in generic three-phase transmission lines, based on the principles of electromagnetic fields. The proposed approach considers different physical configurations of the conductors, as well as the spatial arrangement of the phases, enabling the development of equations applicable to various line topologies. Thus, the research seeks to provide a robust and versatile analytical tool capable of assisting both in the design and optimization of power transmission systems, contributing to the enhancement of their electrical characteristics modeling.