Energy Systems

, Volume 3, Issue 3, pp 221–258 | Cite as

Optimal power flow: a bibliographic survey I

Formulations and deterministic methods
  • Stephen Frank
  • Ingrida Steponavice
  • Steffen RebennackEmail author
Original Paper


Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.


Electric power systems Optimal power flow Optimal power flow formulations Optimal power flow requirements Deterministic optimization Global optimization Nonlinear optimization Survey 


The following summarizes the meanings of abbreviations and acronyms used throughout the paper:


Alternating Current


Active Set and Penalty


Broyden-Fletcher-Goldfarb-Shanno (quasi-Newton method)


Conjugate Gradient


Direct Current


Davidon-Fletcher-Powell (quasi-Newton method)


Extended Conic-Quadratic


High-Voltage Direct Current


Flexible AC Transmission Systems


Generalized Reduced Gradient


Interior Point Method


Karush-Kuhn-Tucker (conditions for optimality)


Linear Programming


Modified Barrier-Augmented Lagrangian


Multiple Centrality Corrections


Mixed Integer Linear Programming


Mixed Integer-Nonlinear Programming




Nonlinear Complementarity


Nonlinear Programming


Optimal Power Flow


Optimal Reactive Power Flow






Primal-Dual Interior Point Method


Primal-Dual Logarithmic Barrier


Quadratic Programming


Reduced Gradient


Security-Constrained Economic Dispatch


Step-Controlled Interior Point Method


Security-Constrained Unit Commitment


Semi-Definite Programming


Sequential Linear Programming


Sequential Quadratic Programming


Trust Region Interior Point Method


Unified Power Flow Controller


Volt-Ampere Reactive


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Stephen Frank
    • 1
  • Ingrida Steponavice
    • 2
  • Steffen Rebennack
    • 3
    Email author
  1. 1.Department of Electrical Engineering and Computer ScienceColorado School of MinesGoldenUSA
  2. 2.Department of Mathematical Information TechnologyUniversity of JyvaskylaAgoraFinland
  3. 3.Division of Economics and BusinessColorado School of MinesGoldenUSA

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