A Power Flow Measure for Unsolvable Cases

Thomas J. Overbye

Research output: Contribution to journalArticlepeer-review


As power systems become more heavily loaded, there will be an increase in the number of situations where the power flow equations have no real solution, particularly in contingency analysis and planning applications. Since these cases can represent the most severe threats to viable system operation, it is important that a computationally efficient technique be developed to both quantify the degree of unsolvability, and to provide optimal recommendations of the parameters to change to return to a solvable solution. Such an algorithm is developed in the paper. The distance in parameter space between the desired operating point and the closest solvable operating point provides a measure of the degree of unsolvability, with the difference between these two points providing the optimal system parameter changes. The algorithm is based upon a Newton-Raphson power flow algorithm, which provides both computational efficiency and compatibility with existing security analysis techniques. The method is demonstrated on systems of up to 118 buses.

Original languageEnglish (US)
Pages (from-to)1359-1365
Number of pages7
JournalIEEE Transactions on Power Systems
Issue number3
StatePublished - Aug 1994
Externally publishedYes


  • Power flow
  • bifurcation
  • power flow
  • security assessment
  • solution existence

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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