Invertibility Conditions for the Admittance Matrices of Balanced Power Systems

TL;DR

This paper investigates the invertibility of admittance matrices in balanced power systems, correcting previous proofs and extending conditions to include lossless branches and transformers with off-nominal tap ratios.

Contribution

It corrects a technical issue in prior invertibility conditions and introduces new, more general conditions applicable to a wider range of power system configurations.

Findings

Corrected previous invertibility proof.

Derived new conditions for lossless and transformer systems.

Extended applicability of invertibility criteria.

Abstract

The admittance matrix encodes the network topology and electrical parameters of a power system in order to relate the current injection and voltage phasors. Since admittance matrices are central to many power engineering analyses, their characteristics are important subjects of theoretical studies. This paper focuses on the key characteristic of \emph{invertibility}. Previous literature has presented an invertibility condition for admittance matrices. This paper first identifies and fixes a technical issue in the proof of this previously presented invertibility condition. This paper then extends this previous work by deriving new conditions that are applicable to a broader class of systems with lossless branches and transformers with off-nominal tap ratios.