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@ARTICLE{Hartmann:1034542,
      author       = {Hartmann, Carsten and Böttcher, Philipp C. and Gross,
                      David and Witthaut, Dirk},
      title        = {{S}ynchronized {S}tates of {P}ower {G}rids and {O}scillator
                      {N}etworks by {C}onvex {O}ptimization},
      journal      = {PRX energy},
      volume       = {3},
      number       = {4},
      address      = {College Park, MD},
      publisher    = {American Physical Society},
      reportid     = {FZJ-2024-07305},
      pages        = {043004},
      year         = {2024},
      abstract     = {Synchronization is essential for the operation of ac power
                      systems: all generators in the power grid must rotate with
                      fixed relative phases to enable a steady flow of electric
                      power. Understanding the conditions for and the limitations
                      of synchronization is of utmost practical importance. In
                      this article, we propose a novel approach to computing and
                      analyzing the stable stationary states of a power grid or a
                      network of Kuramoto oscillators in terms of a convex
                      optimization problem. This approach allows us to
                      systematically compute all stable states where the phase
                      difference across an edge does not exceed 𝜋/2.
                      Furthermore, the optimization formulation allows us to
                      rigorously establish certain properties of synchronized
                      states and to bound the error in the widely used linear
                      power flow approximation.},
      cin          = {ICE-1},
      ddc          = {530},
      cid          = {I:(DE-Juel1)ICE-1-20170217},
      pnm          = {1122 - Design, Operation and Digitalization of the Future
                      Energy Grids (POF4-112) / DFG project G:(GEPRIS)491111487 -
                      Open-Access-Publikationskosten / 2022 - 2024 /
                      Forschungszentrum Jülich (OAPKFZJ) (491111487)},
      pid          = {G:(DE-HGF)POF4-1122 / G:(GEPRIS)491111487},
      typ          = {PUB:(DE-HGF)16},
      doi          = {10.1103/PRXEnergy.3.043004},
      url          = {https://juser.fz-juelich.de/record/1034542},
}