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
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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DOI: https://doi.org/10.1007/s12667-012-0056-y