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.