Zero Duality Gap in Optimal Power Flow Problem

By Javad Lavaei, Steven H. Low. IEEE Transactions on Power Systems, 2012

1,278 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9144938e4ff665638218f29f19cd95894b9c5e74

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Citations in the corpus

New Formulation and Strong MISOCP Relaxations for AC Optimal Transmission Switching Problem (2015, background): “It is demonstrated by several authors that convex relaxations, especially semidefinite programming (SDP) relaxations, of the AC OPF problem provide tight lower bounds on standard IEEE test instances [3, 32, 35, 36].”
Optimal Reactive Power Dispatch for Voltage Regulation in Unbalanced Distribution Systems (2016, neutral): “, [3], [13]–[15] and the references therein).”
PowerModels.J1: An Open-Source Framework for Exploring Power Flow Formulations (2017, background): “Indeed, these emerging methods have demonstrated promising results on a wide range of problem domains, including Optimal Power Flow (OPF) [4], [9], [10], Optimal Transmission Switching (OTS) [6], [11], Transmission Network Expansion Planning (TNEP) [12]–[14], and Micro-Grid Design [15], [16].”
Convex relaxation of optimal power flow: A tutorial (2013, background): “The exactness of SDP relaxation for DC networks is first proved in [49] using a duality argument.”
Application of the Moment-SOS Approach to Global Optimization of the OPF Problem (2013, methodology): “To make the link with the rank relaxation of [2], consider now the case when the varying part of the ’s are quadratic and homogeneous like in [2], that is for all , with symmetric matrices and scalars .”
Optimization of AC Transmission System Planning (2013, methodology): “In recent research on convexifying the OPF formulation, it is shown that solving the SDP problem given by (1a), (2)–(5), (6b), (7a)–(9a), (10c), (10d), and (11b) yields the global OPF solution for a large class of networks, including the IEEE test systems with their smallest branch resistance restri”
Security-Constrained Unit Commitment for AC-DC Grids With Generation and Load Uncertainty (2018, background): “The approaches given in [18] and [23] are not directly applicable to solve problem (24), since we have binary decision variables.”
A Fully Distributed Reactive Power Optimization and Control Method for Active Distribution Networks (2014, background): “Semi-definite relaxation may be used to solve a convex Lagrangian dual problem instead of the primal nonconvex one [10]; this method works in radial networks, but it involves additional large-scale variables and cannot be extended to applications in meshed networks [11].”
A Linearized OPF Model With Reactive Power and Voltage Magnitude: A Pathway to Improve the MW-Only DC OPF (2018, background): “Finding the global optimum of the OPF model is non-deterministic polynomial-time (NP) hard [3].”
Solving Multi-Objective Economic Dispatch Problem Via Semidefinite Programming (2013, methodology): “There are examples of the application of the SDP formulation to the ED and optimal power flow problems [19]–[24].”
A Successive Linear Programming Approach to Solving the IV-ACOPF (2016, background): “Lavaei and Low further prove that if the network is radial, then this sufficient condition always holds [2] and the second order conic relaxation (SOCR) is equivalent for these cases [31]; this can be attributed to the fact that the power flow solution of a radial network is unique [32].”
Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow (2014, background): “— One of the early works that popularizes this approach is [6].”