Available transfer capability calculation using a smoothing pointwise maximum function

Xiaojiao Tong, Felix F. Wu, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)


The determination of the available transfer capability (ATC) is formulated as a problem of finding the solution of a system of equations using the pointwise maximum function, which collapses all operating constraints of the system into one equation. The resulting equations are semismooth. The semismooth equations are solved by the use of a smoothing function. Two solution algorithms are presented. One is a smoothing Newton method in which the smoothing parameter is treated as an independent variable. Another one is a smoothing decoupled Newton method, which incorporates the inherent weak-coupling characteristics of power systems into the algorithm and is suitable for solving large scale problems. The convergence of the two algorithms is studied in detail. A numerical example is presented to illustrate the effectiveness of the proposed methods.
Original languageEnglish
Pages (from-to)462-474
Number of pages13
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number1
Publication statusPublished - 1 Feb 2008


  • Available transfer capability (ATC)
  • Convergence
  • Decoupled method
  • Equations
  • Load flow
  • Mathematical model
  • Pointwise maximum function (PMF)
  • Power systems
  • Security
  • Security region
  • Smoothing methods
  • Smoothing newton method
  • Smoothing Newton method

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


Dive into the research topics of 'Available transfer capability calculation using a smoothing pointwise maximum function'. Together they form a unique fingerprint.

Cite this