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@ARTICLE{Balestra:872568,
      author       = {Balestra, Chiara and Kaiser, Franz and Manik, Debsankha and
                      Witthaut, Dirk},
      title        = {{M}ultistability in lossy power grids and oscillator
                      networks},
      journal      = {Chaos},
      volume       = {29},
      number       = {12},
      issn         = {1089-7682},
      address      = {Woodbury, NY},
      publisher    = {American Institute of Physics},
      reportid     = {FZJ-2020-00074},
      pages        = {123119 -},
      year         = {2019},
      abstract     = {Networks of phase oscillators are studied in various
                      contexts, in particular in the modeling of the electric
                      power grid. A functional grid corresponds to a stable steady
                      state, such that any bifurcation can have catastrophic
                      consequences up to a blackout. But also the existence of
                      multiple steady states is undesirable, as it can lead to
                      transitions or circulatory flows. Despite the high practical
                      importance there is still no general theory of the existence
                      and uniqueness of steady states in such systems. Analytic
                      results are mostly limited to grids without Ohmic losses. In
                      this article, we introduce a method to systematically
                      construct the solutions of the real power load-flow
                      equations in the presence of Ohmic losses and explicitly
                      compute them for tree and ring networks. We investigate
                      different mechanisms leading to multistability and discuss
                      the impact of Ohmic losses on the existence of solutions.},
      cin          = {IEK-STE},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IEK-STE-20101013},
      pnm          = {153 - Assessment of Energy Systems – Addressing Issues of
                      Energy Efficiency and Energy Security (POF3-153) / CoNDyNet
                      2 - Kollektive Nichtlineare Dynamik Komplexer Stromnetze
                      (BMBF-03EK3055B) / ES2050 - Energie Sytem 2050 (ES2050) /
                      VH-NG-1025 - Helmholtz Young Investigators Group
                      "Efficiency, Emergence and Economics of future supply
                      networks" $(VH-NG-1025_20112014)$},
      pid          = {G:(DE-HGF)POF3-153 / G:(DE-JUEL1)BMBF-03EK3055B /
                      G:(DE-HGF)ES2050 / $G:(HGF)VH-NG-1025_20112014$},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:31893663},
      UT           = {WOS:000505563100008},
      doi          = {10.1063/1.5122739},
      url          = {https://juser.fz-juelich.de/record/872568},
}