Convexity of structure preserving energy functions in power transmission: Novel results and applications

Krishnamurthy Dvijotham, Michael Chertkov

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

3 Scopus citations


It is well-known in the power systems literature that the behavior of the transmission power system (under certain simplifying assumptions) can be used to study the post-fault dynamics of a power system and provide principled estimates on dynamic stability margins. In this paper, we study a special feature of the energy function that has previously received little attention: convexity. We prove that the energy function for structure preserving models of power systems is convex under certain reasonable conditions on phases and voltages. Beyond stability analysis, these convexity results have a number of applications, noticeably, building a provably convergent PF solver, which we discuss in detail in this paper. We also outline potential applications to reformulating Optimum Power Flow (OPF), Model Predictive Control (MPC) and identifying the most probable failure (instanton) as convex optimization problems.

Original languageEnglish (US)
Title of host publicationACC 2015 - 2015 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages8
ISBN (Electronic)9781479986842
StatePublished - Jul 28 2015
Externally publishedYes
Event2015 American Control Conference, ACC 2015 - Chicago, United States
Duration: Jul 1 2015Jul 3 2015

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2015 American Control Conference, ACC 2015
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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