A mixed-integer linear programming approach for multi-stage security-constrained transmission expansion planning

Hui Zhang, Vijay Vittal, Gerald Thomas Heydt, Jaime Quintero

Research output: Contribution to journalArticlepeer-review

207 Scopus citations


The transmission expansion planning (TEP) problem in modern power systems is a large-scale, mixed-integer, non-linear and non-convex problem. Although remarkable advances have been made in optimization techniques, finding an optimal solution to a problem of this nature can still be extremely challenging. Based on the linearized power flow model, this paper presents a mixed-integer linear programming (MILP) approach that considers losses, generator costs and the $N - 1$ security constraints for the multi-stage TEP problem. The losses and generator cost are modeled as piecewise linear functions of the line flows and the generator outputs, respectively. The IEEE 24-bus system is used to compare the lossy and the lossless model. The results show that the lossy model provides savings in total cost in the long run. The selection of the best number of piecewise linear sections L is also shown. Then a complete planning framework is presented and a multi-stage TEP is performed on the IEEE 118-bus test system. Simulation results show that the proposed approach is accurate and efficient, and has the potential to be applied to large-scale power system planning problems.

Original languageEnglish (US)
Article number6112698
Pages (from-to)1125-1133
Number of pages9
JournalIEEE Transactions on Power Systems
Issue number2
StatePublished - May 2012


  • $N - 1$ contingency modeling
  • Generator cost modeling
  • loss modeling
  • mixed-integer linear programming
  • piecewise linearization
  • transmission engineering
  • transmission expansion planning

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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