Impact of Negative Reactance on Definiteness of B-Matrix and Feasibility of DC Power Flow


This paper reports an essential phenomenon on the existence of "negative reactance in practical power system models. The negative reactance issue is important, as it could affect the definiteness of the B admittance matrix of power networks and the feasibility of DC power flow. With the graph theory, the B matrix can be treated as a Laplacian matrix. Several theorems and corollaries are given with proof to study the definiteness of the Laplacian matrix with negative weights. Based upon these theorems, the exploration in this paper demonstrates that the negative reactance may even result in "physical dis-connectivity" and make the linear system singular, so that the DC power flow will be infeasible. The results on several test systems show that the location and value of the negative reactance affect the DC power flow feasibility.


Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center

Keywords and Phrases

Eigenvalues and Eigenfunctions; Flow Graphs; Graph Theory; Laplace Transforms; Linear Systems; Matrix Algebra; Admittance Matrices; DC Power Flow; Eigen-Value; Laplacian Matrices; Negative Reactance; Power Networks; Power System Model; Test Systems; Electric Load Flow; Eigenvalue.; Laplacian Matrix

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


File Type





© 2017 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Mar 2019