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@ARTICLE{Hrsch:849931,
      author       = {Hörsch, Jonas and Ronellenfitsch, Henrik and Witthaut,
                      Dirk and Brown, Tom},
      title        = {{L}inear optimal power flow using cycle flows},
      journal      = {Electric power systems research},
      volume       = {158},
      issn         = {0378-7796},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier Science},
      reportid     = {FZJ-2018-04026},
      pages        = {126 - 135},
      year         = {2018},
      abstract     = {Linear optimal power flow (LOPF) algorithms use a
                      linearization of the alternating current (AC) load flow
                      equations to optimize generator dispatch in a network
                      subject to the loading constraints of the network branches.
                      Common algorithms use the voltage angles at the buses as
                      optimization variables, but alternatives can be
                      computationally advantageous. In this article we provide a
                      review of existing methods and describe a new formulation
                      that expresses the loading constraints directly in terms of
                      the flows themselves, using a decomposition of the network
                      graph into a spanning tree and closed cycles. We provide a
                      comprehensive study of the computational performance of the
                      various formulations, in settings that include
                      computationally challenging applications such as
                      multi-period LOPF with storage dispatch and generation
                      capacity expansion. We show that the new formulation of the
                      LOPF solves up to 7 times faster than the angle formulation
                      using a commercial linear programming solver, while another
                      existing cycle-base formulation solves up to 20 times
                      faster, with an average speed-up of factor 3 for the
                      standard networks considered here. If generation capacities
                      are also optimized, the average speed-up rises to a factor
                      of 12, reaching up to factor 213 in a particular instance.
                      The speed-up is largest for networks with many buses and
                      decentral generators throughout the network, which is highly
                      relevant given the rise of distributed renewable generation
                      and the computational challenge of operation and planning in
                      such networks.},
      cin          = {IEK-STE},
      ddc          = {620},
      cid          = {I:(DE-Juel1)IEK-STE-20101013},
      pnm          = {153 - Assessment of Energy Systems – Addressing Issues of
                      Energy Efficiency and Energy Security (POF3-153) /
                      VH-NG-1025 - Helmholtz Young Investigators Group
                      "Efficiency, Emergence and Economics of future supply
                      networks" $(VH-NG-1025_20112014)$ / CoNDyNet - Kollektive
                      Nichtlineare Dynamik Komplexer Stromnetze $(PIK_082017)$},
      pid          = {G:(DE-HGF)POF3-153 / $G:(HGF)VH-NG-1025_20112014$ /
                      $G:(Grant)PIK_082017$},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000428104700012},
      doi          = {10.1016/j.epsr.2017.12.034},
      url          = {https://juser.fz-juelich.de/record/849931},
}