Branch Flow Model: Relaxations and Convexification-Part II

Farivar, M; Low, SH

doi:10.1109/TPWRS.2013.2255318

Title: Branch Flow Model: Relaxations and Convexification-Part II

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Abstract

We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks using phase shifters so that OPF for the convexified network can always be solved efficiently for an optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Part I introduces our branch flow model, explains the two relaxation steps, and proves the conditions for exact relaxation. Part II describes convexification of mesh networks, and presentsmore » simulation results.« less

Authors:: Farivar, M; Low, SH

Publication Date:: Thu Aug 01 00:00:00 EDT 2013

Sponsoring Org.:: USDOE Advanced Research Projects Agency - Energy (ARPA-E)

OSTI Identifier:: 1211444

DOE Contract Number:: DE-AR0000226

Resource Type:: Journal Article

Journal Name:: IEEE Transactions on Power Systems

Additional Journal Information:: Journal Volume: 28; Journal Issue: 3; Journal ID: ISSN 0885-8950

Country of Publication:: United States

Language:: English

Citation Formats


                    Farivar, M, and Low, SH. Branch Flow Model: Relaxations and Convexification-Part II.  United States: N. p., 2013. 
        Web.  doi:10.1109/TPWRS.2013.2255318.

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                    Farivar, M, & Low, SH. Branch Flow Model: Relaxations and Convexification-Part II.  United States.  https://doi.org/10.1109/TPWRS.2013.2255318

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                    Farivar, M, and Low, SH. 2013.  
        "Branch Flow Model: Relaxations and Convexification-Part II".  United States.  https://doi.org/10.1109/TPWRS.2013.2255318.

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@article{osti_1211444,

  title        = {Branch Flow Model: Relaxations and Convexification-Part II},

  author       = {Farivar, M and Low, SH},

  abstractNote = {We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks using phase shifters so that OPF for the convexified network can always be solved efficiently for an optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Part I introduces our branch flow model, explains the two relaxation steps, and proves the conditions for exact relaxation. Part II describes convexification of mesh networks, and presents simulation results.},

  doi          = {10.1109/TPWRS.2013.2255318},

  url          = {https://www.osti.gov/biblio/1211444},
  journal      = {IEEE Transactions on Power Systems},

  issn         = {0885-8950},

  number       = 3,

  volume       = 28,

  place        = {United States},

  year         = {Thu Aug 01 00:00:00 EDT 2013},

  month        = {Thu Aug 01 00:00:00 EDT 2013}

}

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