An Introduction to Optimal Power Flow: Theory, Formulation, and Examples

Stephen Frank, Steffen Rebennack

Research output: Contribution to journalArticlepeer-review

154 Scopus Citations


The set of optimization problems in electric power systems engineering known collectively as Optimal Power Flow (OPF) is one of the most practically important and well-researched subfields of constrained nonlinear optimization. OPF has enjoyed a rich history of research, innovation, and publication since its debut five decades ago. Nevertheless, entry into OPF research is a daunting task for the uninitiated--both due to the sheer volume of literature and because OPF's ubiquity within the electric power systems community has led authors to assume a great deal of prior knowledge that readers unfamiliar with electric power systems may not possess. This article provides an introduction to OPF from an operations research perspective; it describes a complete and concise basis of knowledge for beginning OPF research. The discussion is tailored for the operations researcher who has experience with nonlinear optimization but little knowledge of electrical engineering. Topics covered include power systems modeling, the power flow equations, typical OPF formulations, and common OPF extensions.
Original languageAmerican English
Pages (from-to)1172-1197
Number of pages26
JournalIIE Transactions
Issue number12
StatePublished - 2016

NREL Publication Number

  • NREL/JA-5500-67031


  • electric power systems analysis
  • electrical engineering
  • nonlinear programming
  • operations research
  • optimal power flow
  • optimization
  • power flow


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