Modelling and Kron reduction of power flow networks in directed graphs

TL;DR

This paper introduces a new formulation of the weighted Laplacian matrix for directed graphs, enabling effective Kron reduction in lossless DC power flow networks, validated through simulations of standard IEEE test systems.

Contribution

It proposes a novel weighted Laplacian matrix for directed graphs that accurately models lossless DC power flow networks and establishes conditions for Kron reduction in such systems.

Findings

The new Laplacian matrix is equivalent to the conventional one.

The method is validated on multiple IEEE test systems.

Kron reduction conditions are established for directed graphs.

Abstract

Electrical grids are large-sized complex systems that require strong computing power for monitoring and analysis. Kron reduction is a general reduction method in graph theory and is often used for electrical circuit simplification. In this paper, we propose a novel formulation of the weighted Laplacian matrix for directed graphs. The proposed matrix is proved to be strictly equivalent to the conventionally formulated Laplacian matrix and is verified to well model a lossless DC power flow network in directed graphs. We as well present significant properties of the proposed weighted Laplacian and conditions of Kron reduction in directed graphs and in lossless DC power flow networks. The reduction method is verified via simulation models of IEEE-3, IEEE-5, IEEE-9, IEEE-14, and IEEE RTS-96 test systems.