Semidefinite programming for optimal power flow problems

By Xiaoqing Bai, Hua Wei, K. Fujisawa, Yong Wang. 2008

607 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8cdf8c43ee8b3558ca84b7d634418b04f31e9fc7

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In Electrical and Electronic Engineering

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Citations in the corpus

PowerModels.J1: An Open-Source Framework for Exploring Power Flow Formulations (2017, background): “, Moment-Hierarchy [4], SDP [5], QC [6], SOC [7], CDF [8]), which provide solution quality guarantees and leverage state-of-the-art convex optimization software.”
Solving Multiperiod OPF Problems Using an AC-QP Algorithm Initialized With an SOCP Relaxation (2017, background): “Several examples of these relaxations can be found in [11]–[23].”
Convex relaxation of optimal power flow: A tutorial (2013, background): “An important observation was made in [19], [20] that AC OPF can be formulated as a quadratically constrained quadratic program and therefore can be approximated by a semidefinite program.”
A Linearized OPF Model With Reactive Power and Voltage Magnitude: A Pathway to Improve the MW-Only DC OPF (2018, background): “Approaches include semidefinite programming (SDP) relaxation [3], [6], quadratic programming (QP) relaxation [7], and second-order cone programming (SOCP) relaxation [8], [20].”
Bound Tightening for the Alternating Current Optimal Power Flow Problem (2016, background): “Interest in conic optimization techniques for ACOPF is largely due to multiple reports of zero duality gap for various IEEE power system test cases (see [9], [11], [12]).”
Strong SOCP Relaxations for the Optimal Power Flow Problem (2015, methodology): “In particular, the second-order cone programming (SOCP) and the semidefinite programming (SDP) relaxations are first applied to the OPF problem in Jabr (2006), and Bai et al. (2008), Bai and Wei (2009) and Lavaei and Low (2012).”
The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms (2019, methodology): “These include approximations such as the LPAC [1], IV-Flow [2] and relaxations such as the Second-Order Cone (SOC) [3], Convex-DistFlow (CDF) [4], Quadratic Convex (QC) [5], [6], Semidefinite Programming (SDP) [7], and Moment / Sum-of-Squares Hierarchies [8]– [11], just to name a few.”
Zero Duality Gap in Optimal Power Flow Problem (2012, methodology): “However, [19] drops a rank constraint in the original OPF without any justification in order to obtain a convex formulation.”
A semidefinite programming method with graph partitioning technique for optimal power flow problems (2011, methodology): “Table 2 shows the CPU time and the number of iterations for the optimal solutions by SDP-OPF in [9] for four objective functions of all seven test systems.”
A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems (2017, unknown): “We next present two convex relaxations of the power flow equations: a semidefinite programming (SDP) relaxation of the model (1) for general networks [24], [25], and a second-”
Physics of power networks makes hard optimization problems easy to solve (2012, background): “In order to solve OPF more efficiently, different conic and convex relaxations have been proposed in the past decade [11], [12], [13].”
Moment/Sum-of-Squares Hierarchy for Complex Polynomial Optimization (2015, background): “Since 2006, the ability of the Shor and second-order conic relaxations to find global solutions [3,7,20,34,47,52,69] has been studied.”
Solving Multi-Objective Economic Dispatch Problem Via Semidefinite Programming (2013, background): “Such single-objective ED problems were considered in [19], [21]–[24].”
A Successive Linear Programming Approach to Solving the IV-ACOPF (2016, background): “[30] propose a semidefinite relaxation (SDR) for which Lavaei and Low [2] derive a rank-one sufficient condition under which the SDR is exact, i.”