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

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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 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.

Original languageEnglish
Pages (from-to)2-17
Number of pages15
JournalIEEE Transactions on Automatic Control
Issue number1
Publication statusPublished - 1-Jan-2023


  • constantpower loads
  • DC power grids
  • Mathematical models
  • Power demand
  • Power flow analysis
  • Power grids
  • Power system stability
  • Steady-state
  • Transportation
  • Voltage
  • voltage stability

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