Efficient algorithm for locating and sizing series compensation devices in large power transmission grids: I. Model implementation

Vladimir Frolov, Scott Backhaus, Misha Chertkov

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We explore optimization methods for planning the placement, sizing and operations of flexible alternating current transmission system (FACTS) devices installed to relieve transmission grid congestion. We limit our selection of FACTS devices to series compensation (SC) devices that can be represented by modification of the inductance of transmission lines. Our master optimization problem minimizes the l1 norm of the inductance modification subject to the usual line thermal-limit constraints. We develop heuristics that reduce this non-convex optimization to a succession of linear programs (LP) that are accelerated further using cutting plane methods. The algorithm solves an instance of the MatPower Polish Grid model (3299 lines and 2746 nodes) in 40 seconds per iteration on a standard laptop - a speed that allows the sizing and placement of a family of SC devices to correct a large set of anticipated congestions. We observe that our algorithm finds feasible solutions that are always sparse, i.e., SC devices are placed on only a few lines. In a companion manuscript, we demonstrate our approach on realistically sized networks that suffer congestion from a range of causes, including generator retirement. In this manuscript, we focus on the development of our approach, investigate its structure on a small test system subject to congestion from uniform load growth, and demonstrate computational efficiency on a realistically sized network.

Original languageEnglish (US)
Article number105015
JournalNew Journal of Physics
StatePublished - Oct 24 2014
Externally publishedYes


  • nonconvex optimization
  • power compensation devices
  • power system transmission

ASJC Scopus subject areas

  • General Physics and Astronomy


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