Second-order cone AC optimal power flow: convex relaxations and feasible solutions

Zhao Yuan*, Mohammad Reza Hesamzadeh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


Optimal power flow (OPF) is the fundamental mathematical model to optimize power system operations. Based on conic relaxation, Taylor series expansion and McCormick envelope, we propose three convex OPF models to improve the performance of the second-order cone alternating current OPF (SOC-ACOPF) model. The underlying idea of the proposed SOC-ACOPF models is to drop assumptions of the original SOC-ACOPF model by convex relaxation and approximation methods. A heuristic algorithm to recover feasible ACOPF solution from the relaxed solution of the proposed SOC-ACOPF models is developed. The proposed SOC-ACOPF models are examined through IEEE case studies under various load scenarios and power network congestions. The quality of solutions from the proposed SOC-ACOPF models is evaluated using MATPOWER (local optimality) and LINDOGLOBAL (global optimality). We also compare numerically the proposed SOC-ACOPF models with other two convex ACOPF models in the literature. The numerical results show robust performance of the proposed SOC-ACOPF models and the feasible solution recovery algorithm.

Original languageEnglish
Pages (from-to)268-280
Number of pages13
JournalJournal of Modern Power Systems and Clean Energy
Issue number2
Publication statusPublished - 1 Mar 2019

Bibliographical note

Publisher Copyright:
© 2018, The Author(s).

Other keywords

  • Conic relaxation
  • Feasible solution
  • McCormick envelope
  • Optimal power flow
  • Taylor series expansion


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