Estimating the saddle-node bifurcation point of static power systems using the holomorphic embedding method

Shruti D. Rao, Daniel Tylavsky, Yang Feng

Research output: Contribution to journalArticle

32 Scopus citations


Voltage stability studies have been progressively gaining importance in the power engineering community. Predicting the saddle-node bifurcation point (SNBP) of a power system has become more critical as the power-system loading has increased in many places without a concomitant increase in transmission resources. Since a Newton-Raphson power-flow method is inherently unstable near the SNBP, adaptations such as continuation methods have been used as stabilizers. A new class of nonlinear equation solvers known as the holomorphic embedding method (HEM) is theoretically guaranteed to find the high-voltage solution to the power-flow problem, if one exists, up to the SNBP, provided sufficient precision is used and the conditions of Stahl's theorem are satisfied by the equation set. In this paper, four different HEM-based methods to estimate the saddle-node bifurcation point of a power system, are proposed and compared in terms of accuracy as well as computational efficiency.

Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalInternational Journal of Electrical Power and Energy Systems
StatePublished - Jan 1 2017



  • Analytic continuation
  • Holomorphic embedding
  • Holomorphically embedded power flow method
  • Saddle-node bifurcation point
  • Voltage collapse point
  • Voltage stability

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering

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