DC power grids with constant-power loads -- Part I: A full characterization of power flow feasibility, long-term voltage stability and their correspondence

TL;DR

This paper develops a comprehensive framework for analyzing power flow feasibility and voltage stability in DC power grids with constant-power loads, establishing a complete characterization of feasible demands and stability conditions.

Contribution

It introduces a full characterization of feasible power demands, a novel proof of convexity, and an LMI condition for demand feasibility under perturbations.

Findings

One-to-one correspondence between feasible demands and long-term voltage semi-stable operating points.

Convexity of the set of feasible power demands proven.

A necessary and sufficient LMI condition for demand feasibility under small perturbations.

Abstract

In this two-part paper we develop a unifying framework for the analysis of the feasibility of the power flow equations for DC power grids with constant-power loads. In Part I of this paper we present a detailed introduction to the problem of power flow feasibility of such power grids, and the associated problem of selecting a desirable operating point which satisfies the power flow equations. We introduce and identify all long-term voltage semi-stable operating points, and show that there exists a one-to-one correspondence between such operating points and the constant power demands for which the power flow equations are feasible. Such operating points can be found by solving an initial value problem, and a parametrization of these operating points is also obtained. In addition, we give a full characterization of the set of all feasible power demands, and give a novel proof for the convexity of this set. Moreover, we present a necessary and sufficient LMI condition for the feasibility of a vector of power demands under small perturbation, which extends a necessary condition in the literature.