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@ARTICLE{Kruse:1019421,
      author       = {Kruse, Johannes and Cramer, Eike and Schäfer, Benjamin and
                      Witthaut, Dirk},
      title        = {{P}hysics-{I}nformed {M}achine {L}earning for {P}ower
                      {G}rid {F}requency {M}odeling},
      journal      = {PRX energy},
      volume       = {2},
      number       = {4},
      address      = {College Park, MD},
      publisher    = {American Physical Society},
      reportid     = {FZJ-2023-05378},
      pages        = {043003},
      year         = {2023},
      abstract     = {The operation of power systems is affected by diverse
                      technical, economic, and social factors. Social behavior
                      determines load patterns, electricity markets regulate the
                      generation, and weather-dependent renewables introduce power
                      fluctuations. Thus, power system dynamics must be regarded
                      as a nonautonomous system whose parameters vary strongly
                      with time. However, the external driving factors are usually
                      only available on coarse scales and the actual dependencies
                      of the dynamic system parameters are generally unknown.
                      Here, we propose a physics-informed machine learning model
                      that bridges the gap between large-scale drivers and
                      short-term dynamics of the power system. Integrating
                      stochastic differential equations and artificial neural
                      networks, we construct a probabilistic model of the power
                      grid frequency dynamics in continental Europe. Its
                      probabilistic prediction outperforms the daily average
                      profile, which is an important benchmark, on a time horizon
                      of 15 min. Using the integrated model, we identify and
                      explain the parameters of the dynamical system from the
                      data, which reveal their strong time-dependence and their
                      relation to external drivers such as wind power feed-in and
                      fast generation ramps. Finally, we generate synthetic time
                      series from the model, which successfully reproduce central
                      characteristics of the grid frequency such as their
                      heavy-tailed distribution. All in all, our work emphasizes
                      the importance of modeling power system dynamics as a
                      stochastic nonautonomous system with both intrinsic dynamics
                      and external drivers.},
      cin          = {IEK-10},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IEK-10-20170217},
      pnm          = {1122 - Design, Operation and Digitalization of the Future
                      Energy Grids (POF4-112) / CoNDyNet 2 - Kollektive
                      Nichtlineare Dynamik Komplexer Stromnetze (BMBF-03EK3055B) /
                      HDS LEE - Helmholtz School for Data Science in Life, Earth
                      and Energy (HDS LEE) (HDS-LEE-20190612)},
      pid          = {G:(DE-HGF)POF4-1122 / G:(DE-JUEL1)BMBF-03EK3055B /
                      G:(DE-Juel1)HDS-LEE-20190612},
      typ          = {PUB:(DE-HGF)16},
      doi          = {10.1103/PRXEnergy.2.043003},
      url          = {https://juser.fz-juelich.de/record/1019421},
}