Stability region estimation under low voltage ride through constraints using sum of squares

Chetan Mishra, James S. Thorp, Virgilio A. Centeno, Anamitra Pal

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations


The increasing penetration of inverter based renewable generation (RG) in the form of solar photo-voltaic (PV) or wind has introduced numerous operational challenges and uncertainties. According to the standards [1], [2], these generators are made to trip offline if their operating requirements are not met. In an RG-rich system, this might alter the system dynamics and/or cause shifting of the equilibrium points to the extent that a cascaded tripping scenario is manifested. The present work attempts at avoiding such scenarios by estimating the constrained stability region (CSR) inside which the system must operate using maximal level set of a Lyapunov function estimated through sum of squares (SOS) technique. A time-independent conservative approximation of the LVRT constraint is initially derived for a classical model of the power system. The proposed approach is eventually validated by evaluating the stability of a 3 machine test system with trip-able RG.

Original languageEnglish (US)
Title of host publication2017 North American Power Symposium, NAPS 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781538626993
StatePublished - Nov 13 2017
Event2017 North American Power Symposium, NAPS 2017 - Morgantown, United States
Duration: Sep 17 2017Sep 19 2017


Other2017 North American Power Symposium, NAPS 2017
Country/TerritoryUnited States


  • Constrained stability region (CSR)
  • direct methods
  • low voltage ride through (L VRT)
  • sum of squares (SOS)

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Energy Engineering and Power Technology
  • Control and Optimization
  • Electrical and Electronic Engineering


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