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@ARTICLE{Cramer:905454,
      author       = {Cramer, Eike and Gorjão, Leonardo Rydin and Mitsos,
                      Alexander and Schäfer, Benjamin and Witthaut, Dirk and
                      Dahmen, Manuel},
      title        = {{V}alidation {M}ethods for {E}nergy {T}ime {S}eries
                      {S}cenarios from {D}eep {G}enerative {M}odels},
      reportid     = {FZJ-2022-00695},
      year         = {2021},
      note         = {20 pages, 8 figures, 2 tables},
      abstract     = {The design and operation of modern energy systems are
                      heavily influenced by time-dependent and uncertain
                      parameters, e.g., renewable electricity generation,
                      load-demand, and electricity prices. These are typically
                      represented by a set of discrete realizations known as
                      scenarios. A popular scenario generation approach uses deep
                      generative models (DGM) that allow scenario generation
                      without prior assumptions about the data distribution.
                      However, the validation of generated scenarios is difficult,
                      and a comprehensive discussion about appropriate validation
                      methods is currently lacking. To start this discussion, we
                      provide a critical assessment of the currently used
                      validation methods in the energy scenario generation
                      literature. In particular, we assess validation methods
                      based on probability density, auto-correlation, and power
                      spectral density. Furthermore, we propose using the
                      multifractal detrended fluctuation analysis (MFDFA) as an
                      additional validation method for non-trivial features like
                      peaks, bursts, and plateaus. As representative examples, we
                      train generative adversarial networks (GANs), Wasserstein
                      GANs (WGANs), and variational autoencoders (VAEs) on two
                      renewable power generation time series (photovoltaic and
                      wind from Germany in 2013 to 2015) and an intra-day
                      electricity price time series form the European Energy
                      Exchange in 2017 to 2019. We apply the four validation
                      methods to both the historical and the generated data and
                      discuss the interpretation of validation results as well as
                      common mistakes, pitfalls, and limitations of the validation
                      methods. Our assessment shows that no single method
                      sufficiently characterizes a scenario but ideally validation
                      should include multiple methods and be interpreted carefully
                      in the context of scenarios over short time periods.},
      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       = {2110.14451},
      howpublished = {arXiv:2110.14451},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2110.14451;\%\%$},
      url          = {https://juser.fz-juelich.de/record/905454},
}