A second-order cone model of transmission planning with alternating and direct current lines

Antoine Lesage-Landry, Joshua A. Taylor

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We construct a model for transmission planning with both alternating and direct current lines, the latter of which can be interfaced via either line-commutated converters or voltage-source converters. The transmission expansion problem is nonlinear and nonconvex. Thus, nonlinear solvers cannot guarantee their convergence to the global optimum of the problem. We use relaxations and approximations to formulate a mixed-integer second-order cone transmission expansion model, which can be solved to optimality by current industrial solvers. We base our formulation on the branch flow relaxation. We include losses and reactive power placement, and consider direct current lines connected by both line-commutated converters and voltage-sourced converters. We show that our approach lowers the expansion cost on 6-bus and 24-bus system examples. We evaluate the feasibility of our formulation using a semidefinite relaxation of optimal power flow and find that the resulting plan admits feasible or close to feasible power flows.

Original languageEnglish (US)
Pages (from-to)174-185
Number of pages12
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - Feb 16 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management
  • Industrial and Manufacturing Engineering


  • Convex relaxation
  • Electric power systems
  • Mixed-integer second-order cone programming
  • OR in energy
  • Transmission expansion planning


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