Optimal power flow: a bibliographic survey I

Formulations and deterministic methods

Abstract

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.

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Notes

  1. 1.

    DC power flow is so named because the resulting equations resemble the behavior of direct current systems. However, it still represents the operation of an AC electrical network.

Abbreviations

AC:

Alternating Current

ASP:

Active Set and Penalty

BFGS:

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

CG:

Conjugate Gradient

DC:

Direct Current

DFP:

Davidon-Fletcher-Powell (quasi-Newton method)

ECQ:

Extended Conic-Quadratic

HVDC:

High-Voltage Direct Current

FACTS:

Flexible AC Transmission Systems

GRG:

Generalized Reduced Gradient

IPM:

Interior Point Method

KKT:

Karush-Kuhn-Tucker (conditions for optimality)

LP:

Linear Programming

MBAL:

Modified Barrier-Augmented Lagrangian

MCC:

Multiple Centrality Corrections

MILP:

Mixed Integer Linear Programming

MINLP:

Mixed Integer-Nonlinear Programming

MW:

Megawatt

NC:

Nonlinear Complementarity

NLP:

Nonlinear Programming

OPF:

Optimal Power Flow

ORPF:

Optimal Reactive Power Flow

PC:

Predictor-Corrector

PD:

Primal-Dual

PDIPM:

Primal-Dual Interior Point Method

PDLB:

Primal-Dual Logarithmic Barrier

QP:

Quadratic Programming

RG:

Reduced Gradient

SCED:

Security-Constrained Economic Dispatch

SCIPM:

Step-Controlled Interior Point Method

SCUC:

Security-Constrained Unit Commitment

SDP:

Semi-Definite Programming

SLP:

Sequential Linear Programming

SQP:

Sequential Quadratic Programming

TRIPM:

Trust Region Interior Point Method

UPFC:

Unified Power Flow Controller

VAR:

Volt-Ampere Reactive

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Frank, S., Steponavice, I. & Rebennack, S. Optimal power flow: a bibliographic survey I. Energy Syst 3, 221–258 (2012). https://doi.org/10.1007/s12667-012-0056-y

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Keywords

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