Solvability and stability of a power system DAE model

Tjorben Groß, Stephan Trenn*, Andreas Wirsen

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

8 Citations (Scopus)


The dynamic model of a power system is the combination of the power flow equations and the dynamic description of the generators (the swing equations) resulting in a differential–algebraic equation (DAE). For general DAEs solvability is not guaranteed in general, in the linear case the coefficient matrices have to satisfy a certain regularity condition. We derive a solvability characterization for the linearized power system DAE solely in terms of the network topology. As an extension to previous result we allow for higher order generator dynamics. Furthermore, we show that any solvable power system DAE is automatically of index one, which means that it is also numerically well posed. Finally, we show that any solvable power system DAE is stable but not asymptotically stable.
Original languageEnglish
Pages (from-to)12-17
Number of pages6
JournalSystems and Control Letters
Publication statusPublished - 1-Nov-2016
Externally publishedYes


  • DAE
  • Power systems
  • Solvability
  • Stability

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