# On the Properties of the Power Systems Nodal Admittance Matrix

## TL;DR

This paper investigates the mathematical properties of the nodal admittance matrix in AC power networks, focusing on its rank conditions and implications for network reduction techniques.

## Contribution

It establishes new conditions for the rank of the nodal admittance matrix and explores their implications for Kron Reduction and hybrid network parameters.

## Key findings

- Derived conditions for the rank of the admittance matrix.
- Analyzed the impact on Kron Reduction.
- Discussed implications for hybrid network parameters.

## Abstract

This letter provides conditions determining the rank of the nodal admittance matrix, and arbitrary block partitions of it, for connected AC power networks with complex admittances. Furthermore, some implications of these properties concerning Kron Reduction and Hybrid Network Parameters are outlined.