Improving Optimal Power Flow Relaxations Using 3-Cycle Second-Order Cone\n Constraints

2021/04/14 by Frederik Geth, James Foster, Geth, Frederik +1
Decision Sciences · Engineering · #Advanced Optical Network Technologies #Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Optimal Power Flow Distribution #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #VLSI and FPGA Design Techniques #and Science (cs.CE)

paper · pdf · doi:10.48550/arxiv.2104.06695

openalex publication_date 2021/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper develops a novel second order cone relaxation of the semidefinite\nprogramming formulation of optimal power flow, that does not imply the `angle\nrelaxation'. We build on a technique developed by Kim et al., extend it for\ncomplex matrices, and apply it to 3x3 positive semidefinite matrices to\ngenerate novel second-order cone constraints that augment upon the well-known\n2x2 principal-minor based second-order cone constraints. Finally, we apply it\nto optimal power flow in meshed networks and provide numerical illustrations.\n

Citations

• On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
• The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms

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