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@ARTICLE{Cramer:905464,
      author       = {Cramer, Eike and Mitsos, Alexander and Tempone, Raul and
                      Dahmen, Manuel},
      title        = {{P}rincipal {C}omponent {D}ensity {E}stimation for
                      {S}cenario {G}eneration {U}sing {N}ormalizing {F}lows},
      reportid     = {FZJ-2022-00705},
      year         = {2021},
      note         = {18 pages, 7 figures},
      abstract     = {Neural networks-based learning of the distribution of
                      non-dispatchable renewable electricity generation from
                      sources such as photovoltaics (PV) and wind as well as load
                      demands has recently gained attention. Normalizing flow
                      density models are particularly well suited for this task
                      due to the training through direct log-likelihood
                      maximization. However, research from the field of image
                      generation has shown that standard normalizing flows can
                      only learn smeared-out versions of manifold distributions.
                      Previous works on normalizing flow-based scenario generation
                      do not address this issue, and the smeared-out distributions
                      result in the sampling of noisy time series. In this paper,
                      we exploit the isometry of the principal component analysis
                      (PCA), which sets up the normalizing flow in a
                      lower-dimensional space while maintaining the direct and
                      computationally efficient likelihood maximization. We train
                      the resulting principal component flow (PCF) on data of PV
                      and wind power generation as well as load demand in Germany
                      in the years 2013 to 2015. The results of this investigation
                      show that the PCF preserves critical features of the
                      original distributions, such as the probability density and
                      frequency behavior of the time series. The application of
                      the PCF is, however, not limited to renewable power
                      generation but rather extends to any data set, time series,
                      or otherwise, which can be efficiently reduced using PCA.},
      cin          = {IEK-10},
      cid          = {I:(DE-Juel1)IEK-10-20170217},
      pnm          = {1121 - Digitalization and Systems Technology for
                      Flexibility Solutions (POF4-112) / HDS LEE - Helmholtz
                      School for Data Science in Life, Earth and Energy (HDS LEE)
                      (HDS-LEE-20190612)},
      pid          = {G:(DE-HGF)POF4-1121 / G:(DE-Juel1)HDS-LEE-20190612},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2104.10410},
      howpublished = {arXiv:2104.10410},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2104.10410;\%\%$},
      doi          = {10.1017/dce.2022.7},
      url          = {https://juser.fz-juelich.de/record/905464},
}