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\title{\vspace{-1.7cm}
  Integrated Modelling
  of Energy Systems and Transmission Networks
}
%\subtitle{---}
\author{
  Tom Brown\\
  \emph{Frankfurt Institute for Advanced Studies (FIAS), University of Frankfurt}
}


\date{\vspace{0.3cm}INTEEVER Workshop, Frankfurt, 14th November 2017}


\titlegraphic{%
  \vspace{4.9cm}
  % left bottom right top
  \includegraphics[trim=0 0cm 0 0cm,width=5.5cm,clip=true]{fias-web-official}
  \hspace{3cm}
  \includegraphics[width=4.5cm]{condynet}

  \raggedleft \scriptsize Financed by German Federal Ministry of Education and Research (BMBF)
under grant no. 03SF0472C
}

\begin{document}

\maketitle




\begin{frame}
  \frametitle{The Challenges: Complexity in Energy System Models}


\begin{columns}[T]
\begin{column}{6.5cm}


  \vspace{0.3cm}
\centering

%\includegraphics[width=4cm]{line-loading}
\includegraphics[width=7cm]{pypsa-eur-grid}

\end{column}
\begin{column}{7cm}
    To \alert{decarbonise} the energy system by 2050:
  \begin{itemize}
  \item Need to model \alert{capacity investments} and
    \alert{operation} of all generators, storage, grids and
    heating/transport/industry.
  \item Need \alert{European scope} for smoothing renewables and energy markets.
  \item Need \alert{detailed grid model} to capture network bottlenecks.
  \item Need \alert{all energy sectors} to leverage potential flexibility.
  \end{itemize}
\end{column}
\end{columns}


\source{PyPSA-Eur, based on ENTSO-E map}
\end{frame}



\begin{frame}
  \frametitle{Some solutions from FIAS, Frankfurt}

  \begin{itemize}
  \item \alert{Openness} and \alert{cooperation}
    in the community: engagement with Open Energy Modelling Initiative, development of free software (PyPSA) and open
    data (PyPSA-Eur).
  \item \alert{Clustering algorithms} to reduce the size of the grid model while maintaining important bottlenecks.
  \item \alert{Iterative algorithms for network expansion} that are only near-optimal but fast and stable.
  \item \alert{New formulations of linear OPF problems} that also enhance speed.
  \end{itemize}

  These solutions and techniques will be further expanded and
  developed in a Helmholtz Young Investigator Group starting at KIT
  Institut für Angewandte Informatik (IAI) from April 2018.
\end{frame}


\begin{frame}
  \frametitle{Python for Power System Analysis (PyPSA)}



\begin{columns}[T]
\begin{column}{6.5cm}
  \begin{itemize}

  \item Developed at \href{https://fias.uni-frankfurt.de/}{Frankfurt
    Institute of Advanced Studies} by Tom Brown, Jonas Hörsch and
  David Schlactberger for the \href{http://condynet.de/}{CoNDyNet
    project}.
  \item Fills missing gap between \alert{load flow software} (e.g. MATPOWER,
    PowerFactory) and \alert{energy system simulation software} (e.g. OSeMOSYS, PLEXOS, TIMES).
  \item Good grid modelling is increasingly important, for integration of renewables and possible electrification of transport and heating.
  \end{itemize}
\end{column}
\begin{column}{7cm}

\centering

%\includegraphics[width=4cm]{line-loading}
\includegraphics[width=7cm]{reactive-power}

\end{column}
\end{columns}

\end{frame}




\begin{frame}
  \frametitle{Python for Power System Analysis (PyPSA)}

  The FIAS software PyPSA is online at \url{https://pypsa.org/} and on
  github. It can do:



\begin{columns}[T]
  \begin{column}{6cm}

  \begin{itemize}
  \item Static \alert{power flow}
    \item \alert{Linear optimal power flow} (multiple periods, unit commitment, storage, coupling to other sectors)
    \item \alert{Security-constrained linear optimal power flow}
    \item Total electricity system \alert{investment optimisation}
  \end{itemize}

  \end{column}

\begin{column}{7cm}

  \vspace{0.3cm}
\centering
\includegraphics[width=8cm]{lmp}


\end{column}
\end{columns}

\end{frame}


\begin{frame}
  \frametitle{PyPSA-Eur: Open Model of European Transmission System}
\begin{columns}[T]
\begin{column}{6cm}


  \vspace{0.4cm}
\centering

%\includegraphics[width=4cm]{line-loading}
\includegraphics[width=7cm]{pypsa-eur-grid}
\end{column}
\begin{column}{7.5cm}

  \begin{itemize}
    \item Grid data based on \alert{GridKit} extraction of ENTSO-E interactive map.
    \item FIAS \alert{powerplantmatching} database of power plants in Europe.
    \item Renewable energy time series from open \alert{atlite}, based
      on Aarhus University REatlas.
    \item Geographic \alert{potentials} for RE from land use.
    \item Basic \alert{validation} described in Hörsch et al `PyPSA-Eur: An Open Optimisation Model of the
      European Transmission System'.
    \item \url{https://github.com/FRESNA/pypsa-eur}
  \end{itemize}
\end{column}
\end{columns}

\end{frame}


\begin{frame}
  \frametitle{Network Clustering}

  Can cluster down the network, to reduce resolution while retaining important transmission lines:
\centering
\begin{columns}[T]
  \begin{column}{5cm}

    \centering
    \includegraphics[width=4.1cm]{clustering}
    \includegraphics[width=4.1cm]{full}
  \end{column}
  \begin{column}{5cm}
        \centering
    \includegraphics[width=4.1cm]{256}
        \includegraphics[width=4.1cm]{37}
  \end{column}
\end{columns}


\end{frame}


\begin{frame}
  \frametitle{Clustering: Many algorithms in the literature}

  There are lots of algorithms for aggregating networks, particularly in the engineering literature:
  \begin{itemize}
    \item $k$-means clustering on (electrical) distance
    \item $k$-means on load distribution
    \item Community clustering (e.g. Louvain)
    \item Spectral analysis of Laplacian matrix
    \item Clustering of Locational Marginal Prices with nodal pricing (sees congestion and RE generation)
    \item PTDF clustering
    \item Cluster nodes with correlated RE time series
  \end{itemize}

  The algorithms all serve different purposes (e.g. reducing part of
  the network on the boundary, to focus on another part). Not always tested on real network data.
\end{frame}


\begin{frame}
  \frametitle{Question of spatial resolution}

  If we do a \alert{joint optimisation} of generation, storage and
  transmission with a 95\% \co2 reduction compared to 1990, how is the
  solution affected by an \alert{increase of spatial resolution} in each
  country?

  We expect
  \begin{itemize}
  \item \alert{Better representation of existing internal bottlenecks} that will prevent the transport of e.g. offshore wind to the South of Germany.
  \item \alert{Better local exploitation of good renewable resources}, e.g. local areas of good wind can be better exploited by the optimisation.
  \end{itemize}

  Which effect will win?

  First we only optimize the gas, wind and solar generation
  capacities, the long-term and short-term storage capacities and
  their economic dispatch including the available hydro facilities
  \alert{without grid expansion}.
\end{frame}



\begin{frame}
  \frametitle{Nodal capacities per technology (w/o grid expansion)}

  \includegraphics[width=15cm]{legend-flat}
\begin{columns}[T]
\begin{column}{8cm}


  \includegraphics[trim=0 0cm 0 2cm,width=8cm]{euro-pie-pre-7-branch_limit-1-37.png}

\end{column}
\begin{column}{8cm}

  \raisebox{-6.6cm}{

  \includegraphics[trim=0 0cm 0 2cm,width=8cm]{euro-pie-pre-7-branch_limit-1-256.png}
  }

\end{column}

\end{columns}


\end{frame}



\begin{frame}
   \frametitle{Costs: System cost w/o grid expansion}


\begin{columns}[T]
\begin{column}{8.5cm}
  \includegraphics[width=9.5cm]{cost_eu_1}
\end{column}
\begin{column}{6cm}

  \vspace{2cm}

  \begin{itemize}
  \item Steady total system cost at \euro~260 billion per year
   \item This translates to \euro~82/MWh (compared to today of \euro~50/MWh to \euro~60/MWh)
  \end{itemize}
\end{column}
\end{columns}

\end{frame}


\begin{frame}
  \frametitle{Costs: System cost and break-down into technologies {\large (w/o grid expansion)}}
\begin{columns}[T]
\begin{column}{8.5cm}
  \includegraphics[width=8.5cm]{cost_eu_breakdown_by_cap-1}
\end{column}
\begin{column}{6cm}
  \vspace{.5cm}
  If we break this down into technologies:
  \begin{itemize}
  \item 37 clusters captures around half of total network volume
  \item Redistribution of capacities from offshore wind to solar
  \item Increasing solar share is accompanied by an increase of
    battery storage
  \item Single countries do not stay so stable
  \end{itemize}
\end{column}
\end{columns}
\end{frame}



\begin{frame}
  \frametitle{Interaction between network expansion, cost and spatial scale}



  To investigate how \alert{public acceptance problems} for
  transmission lines impact on the cost-effectiveness, we introduce
  \alert{transmission volume limits}.

  \vspace{0.2cm}

  If each line $\ell$ has length $d_\ell$ and capacity $\bar{P}_\ell$ then:
  \begin{align*}
    \bar P_\ell \hspace{0.2cm} & \geq \hspace{0.2cm} \bar P_\ell^{\mathrm{today}} \\
    \sum_\ell d_\ell \bar P_\ell\hspace{0.2cm}  & \leq \hspace{0.2cm} \mathrm{CAP}_{\mathrm{trans}}\hspace{2cm} \leftrightarrow \hspace{0.5cm} \mu_{\textrm{trans}}
  \end{align*}


  We constrain the
  overall transmission line volume in relation to today's line volume $\mathrm{CAP}_{\mathrm{trans}}^{\mathrm{today}}$:
  \begin{equation*}
    \mathrm{CAP}_{\mathrm{trans}} = x \, \mathrm{CAP}_{\mathrm{trans}}^{\mathrm{today}}
  \end{equation*}
  for $x = 1$ (today's grid) $x = 1.125,1.25,1.5,2,x=3$.

 This allows us to assess the costs of balancing power in time (i.e. storage) versus space (i.e. inter-connecting transmission networks).

\end{frame}


\begin{frame}
  \frametitle{When grid expansion allowed: avoid costly storage}
  \includegraphics[width=15cm]{legend-flat}
  \begin{columns}[T]

\begin{column}{8cm}

  \includegraphics[trim=0 0cm 0 2cm,width=8cm]{euro-pie-pre-7-branch_limit-1-5-256.png}

\end{column}
\begin{column}{8cm}

  \raisebox{-6.6cm}{

  \includegraphics[trim=0 0cm 0 2cm,width=8cm]{euro-pie-pre-7-branch_limit-3-256.png}
  }

\end{column}

\end{columns}


\end{frame}


\begin{frame}
  \frametitle{Costs: Total system cost}

\centering

\begin{columns}[T]
\begin{column}{8.5cm}

    \vspace{0.5cm}

  \includegraphics[width=9cm]{pre-7-costs-total}

\end{column}
\begin{column}{7cm}

  \begin{itemize}
  \item Steady cost for No Expansion (1)
  \item For expansion scenarios, as clusters increase, the better expoitation of good sites decreases costs faster than transmission bottlenecks increase them
  \item Decrease in cost is v. non-linear as grid expanded (25\% grid expansion gives 50\% of optimal cost reduction)
  \item Only a moderate $20-25\%$ increase in costs from the Optimal Expansion
    scenario (3) to the No Expansion scenario (1).
  \end{itemize}

\end{column}

\end{columns}

\end{frame}


\begin{frame}
  \frametitle{Costs: Break-down into technologies}

\centering

  \includegraphics[width=12cm]{cost_eu_breakdown_by_cap}
\end{frame}



\begin{frame}
  \frametitle{Behaviour as transmission expansion is allowed}


\begin{columns}[T]
\begin{column}{8.5cm}
\centering
  \includegraphics[width=8.5cm]{costs_per_cluster_181}
  %\includegraphics[width=6cm]{pre-2-costs_de_storage}
\end{column}
\begin{column}{6cm}
  \begin{itemize}
%\item   %Big reduction in curtailment
    \item Big \alert{non-linear cost reduction} as grid is expanded, from 82\euro/MWh to 66\euro/MWh (drop of 50~bill.~\euro/a)
      \item Most of cost reduction happens with \alert{25\% grid expansion} compared to today's grid; costs
        rather flat once capacity has doubled
      \item Need for solar and batteries decrease significantly as
        grid expanded; with cost-optimal grid, system is dominated by
        wind
  \end{itemize}
\end{column}
\end{columns}
\source{\href{https://doi.org/10.1016/j.energy.2017.06.004}{Schlachtberger et al, 2017}, \href{https://doi.org/10.1109/EEM.2017.7982024}{Hörsch et al, 2017}}
\end{frame}


\begin{frame}
  \frametitle{Grid expansion CAP shadow price for 181 nodes as CAP relaxed}


\begin{columns}[T]
\begin{column}{10cm}
\centering
  \includegraphics[width=11cm]{shadows-branch_limit}
  %\includegraphics[width=6cm]{pre-2-costs_de_storage}
\end{column}
\begin{column}{4cm}
  \begin{itemize}
%\item   %Big reduction in curtailment
  \item With overhead lines the optimal system has around 3 times today's transmission volume
  \item With underground cables (5-8 times more expensive) the optimal system has around 1.3 to 1.6 times today's transmission volume
  \end{itemize}
\end{column}
\end{columns}

\end{frame}




\begin{frame}
  \frametitle{Locational Marginal Prices CAP=1 versus CAP=3}



  \begin{columns}[T]

\begin{column}{8cm}

  \hspace{1cm}  With today's capacities:

  \includegraphics[width=8cm]{lmp-1-256.pdf}

\end{column}
\begin{column}{8cm}

  \hspace{1cm}With three times today's grid:

  \includegraphics[width=8cm]{lmp-3-256.pdf}

\end{column}

\end{columns}


\end{frame}



\begin{frame}
  \frametitle{Iterative grid expansion optimisation}


  The full grid expansion problem has to take account of:
  \begin{itemize}
  \item Non-linear equations for active and reactive power flow ($S_i = \sum_{j} V_i Y_{ij}^* V_j^*$)
  \item Non-linear expansion equations (coupling between changing $Y_{ij}$ and $V_i$)
    \item Integer variables for each additional circuit
      \item Non-convexity of feasible space
    \item Reactive power compensation
     \item Optimal switching
    \item Contingencies ($n-1$, etc.)
  \end{itemize}

  In practice, this level of detail is \alert{redundant} for long-term
  planning at an aggregated level of detail. There are bigger uncertainties elsewhere...

\end{frame}


\begin{frame}
  \frametitle{Even linearisation is too complex for large grids}

  Many transmission planning models use a linearized power flow
  approximation, but even this results in an expansion problem which
  is both \alert{bilinear} and \alert{integer}:
  \begin{align*}
    f_\ell & = b_\ell \cdot \eta_{l} \cdot (\theta_i - \theta_j) \\
    |f_\ell| & \leq \eta_l \cdot F_{\ell}
  \end{align*}
  where $b_\ell$ is the fixed susceptance per circuit, $\theta_i$ is
  the nodal voltage angle and $\eta_\ell \in \{0,1,2,\dots\}$ is the
  integer number of circuits.

  This can be converted to a MILP using a big-$M$ disjunctive
  relaxation. This has been implemented in PyPSA by a researcher from
  TU Delft, but it's very slow.

  There are also MISOC and MISD variants which use convex quadratic
  flow approximations to get more of the physics.

\end{frame}

\begin{frame}
  \frametitle{Iterative grid expansion optimisation}

  \alert{Our approach}: allow each corridor to expand
  \alert{continuously}, i.e. fuse
  \begin{align*}
    b_\ell \cdot \eta_{l} & \to \tilde{b}_\ell  \in \mathbb{R}\\
    \eta_l \cdot F_{\ell} & \to   \tilde{F}_{\ell} \in \mathbb{R}
  \end{align*}
  to continuous variables. This removes the \alert{discreteness}.

  \alert{Algorithm}: Fix $\tilde{b}_\ell$ for the simulation, allow
  $\tilde{F}_{\ell}$ to be optimised, then update $\tilde{b}_\ell$ with the value
  corresponding to the optimised $\tilde{F}_\ell$ ($\tilde{b}_\ell\propto \tilde{F}_\ell$). Repeat until there
  is convergence. This removes the \alert{bilinearity}.

  Approach tested in
  \href{https://doi.org/10.1016/j.energy.2014.01.025}{Hagspiel et al,
    Energy (2014)}.

  The \alert{good}: fast, stable, convergent, feasible, optimal for small networks.

  The \alert{bad}: no guarantee of optimality, must do discretisation into
  circuits `post facto', tricky to build new network topologies.

\end{frame}


\begin{frame}
  \frametitle{Non-linear check of linear results}




\begin{columns}[T]
\begin{column}{7cm}

  \vspace{.2cm}

  In \href{https://doi.org/10.1049/iet-rpg.2015.0135}{Brown et al, IET
    RPG (2016)} we ran the results of a linear grid capacity
  optimisation through a non-linear `AC' power flow:

  \vspace{.2cm}

\includegraphics[width=7.5cm]{gp-duration_curve.pdf}

\end{column}
\begin{column}{6.5cm}


  \begin{itemize}
  \item The `DC' results plateau at 70\% because this was our chosen
    contingency buffer
  \item 70\% is the natural loading level of a typical transmission
    line, which explains the `AC' results: below 70\% the line is a
    capacitor, whereas above 70\% the line behaves like an
    inductor and the loading increases $\propto I^2$.
 \item Conclusion: keeping 70\% contingency limit also solves problems
   with over-loading due to reactive power currents.
  \end{itemize}

\end{column}
\end{columns}




\end{frame}



\begin{frame}
  \frametitle{Cycle formulation of linear power flow}

  We can use dual graph theory to decompose the flows in the network into two parts:
  \begin{enumerate}
  \item A flow on a spanning tree of the network, uniquely determined by nodal $\mathbf{p}$ (ensuring KCL)
  \item Cycle flows, which don't affect KCL; their strength is fixed by enforcing KVL
  \end{enumerate}

\begin{circuitikz}
  \draw
  (0,3)
  to [short,i^=$f_1$,*-*] (3,3)
  to [short,i>=$f_2$,*-*] (3,0)
  to [short,i>=$f_3$,*-*] (0,0)
  to [short,i>=$f_4$,*-*] (0,3);
  \draw (3,3)   to [short,i^=$f_5$,*-*] (0,0);

  \draw (1.5,-1.2) node{$f_\ell$};


  \draw (4,1.5) node{$=$};

  \draw (4,-1.2) node{$=$};


  \draw[red]
  (5,3)
  to [short,i^=$t_1$,*-*] (8,3)
  to [short,i>=$t_2$,*-*] (8,0)
  to [short,i>=$t_3$,*-*] (5,0);

  \draw (6.5,-1.2) node{$t_\ell$};


  \draw (9,1.5) node{$+$};

  \draw (9,-1.2) node{$+$};



  \draw[blue]
  (10,3)
  to [short,i>=$$,*-*] (12.8,3)
  to [short,i>=$$,*-*] (10,0.2)
  to [short,i>=$c_1$,*-*] (10,3);

  \draw[blue]
  (13,0)
  to [short,i>=$$,*-*] (10.2,0)
  to [short,i>=$$,*-*] (13,2.8)
  to [short,i>=$c_2$,*-*] (13,0);


  \draw (11.5,-1.2) node{$\sum_k C_{\ell,k} c_k$};


\end{circuitikz}


\end{frame}




\begin{frame}
  \frametitle{LOPF speedup with cycle flows}
\begin{columns}[T]
  \begin{column}{7cm}
  \includegraphics[width=7.5cm]{lopf-ne-speedup-per-nodes-mean-with-ci-99-regression}
  \end{column}
  \begin{column}{6cm}
    \vspace{0.5cm}
    Using \alert{cycle flows instead of voltage angles} we found for generation expansion optimisation (fixed grid):
    \begin{itemize}
    \item A speed-up of up to \alert{200 times}
    \item Average speed-up of \alert{factor 12}
    \item Speed-up is highest for \alert{large networks with lots of renewables}
    \end{itemize}
  \end{column}

\end{columns}


  \footnotesize
H.~Ronellenfitsch, D.~Manik, J.~Hörsch, {\bf T.~Brown, D.~Witthaut}, \emph{``Dual theory of transmission line outages,''} 2017, IEEE Transactions on Power Systems

J.~Hörsch, H.~Ronellenfitsch, {\bf D.~Witthaut, T.~Brown}, \emph{``Linear Optimal Power Flow Using Cycle Flows,''} 2017

\end{frame}


\begin{frame}
  \frametitle{Coupling to Other Energy Sectors}

  \centering
  \includegraphics[width=13cm]{sector}
\end{frame}



\begin{frame}
  \frametitle{Coupling to Other Energy Sectors}

  \alert{Idea}: Couple the electricity sector to heating and mobility.

  This enables decarbonisation of these sectors \alert{and} offers more flexibility to the power system.

  \vspace{0.2cm}

  \begin{columns}[T]
\begin{column}{6cm}
  \alert{Battery electric vehicles} can change their charging pattern to benefit the
  system and even feed back into the grid if necessary

  \includegraphics[trim=0 0cm 0 0cm,width=6cm,clip=true]{tesla}
\end{column}
\begin{column}{6cm}
  \alert{Heat} is much easier and cheaper to store than electricity, even over many months

  \vspace{0.5cm}

        \includegraphics[trim=0 0cm 0 0cm,width=6cm,clip=true]{pit-zoom}
\end{column}
\end{columns}



\end{frame}


\begin{frame}
  \frametitle{Coupling to Other Energy Sectors}



\begin{columns}[T]

\begin{column}{7.5cm}
  \vspace{0.5cm}
 \includegraphics[width=8.5cm]{costs-bars-cross-1-0-highlights}

\end{column}
  \begin{column}{6.5cm}
    \begin{itemize}
    \item Not just electricity: transport, heating and industrial must
      be considered to meet \alert{Paris targets}
    \item Electrifying land-based transport and low-temperature
      heating would \alert{increase electricity demand} by up to 60\%,
      with strong seasonality
    \item However, these other sectors also offer significant
      \alert{flexibility}: smart battery electric vehicle charging and
      thermal storage can play a big role
  \end{itemize}
  \end{column}
\end{columns}


\end{frame}




\begin{frame}
  \frametitle{PyPSA users}

  PyPSA is being actively used by more than a dozen research institutions and companies (that we
  know of...). Those whose activity is visible online:
  \begin{itemize}
  \item FIAS: Optimisation of European energy system
  \item FIAS+CSIR: Optimisation of South African energy system
  \item RLI, DLR VE, Flensburg, Magdeburg: open\_Ego for open grid optimization
  \item Forschungszentrum Jülich: Optimisation of European energy system
  \item Aarhus University: Optimisation of European energy system
  \item TU Delft: European Northern Seas offshore grid
  \item ewi Energy Research \& Scenarios: Incentives for wind placement in Germany
  \item Saudi Aramco: High renewable scenarios for Saudia Arabia
  \item Edison Energy, Spire in United States
  \end{itemize}

  %Wuppertal Institut??

\end{frame}



\begin{frame}
  \frametitle{PyPSA users}

  The website has been visited by people from 120+
  countries:

  \centering
  \includegraphics[width=11cm]{pypsa-170322}

\end{frame}


\begin{frame}
  \frametitle{PyPSA development}

  \begin{itemize}
  \item Improvements to power flow: distributed slack, reactive power limits
  \item Improvements to OPF: investment over multiple years, non-linear constraints
  \item Workflow: integrate with snakemake
  \item Pyomo: persistent gurobipy solver interface for repeated solution of similar problems
  \item Julia interface port: testing JuMP for more performant problem building
  \end{itemize}

\end{frame}

\begin{frame}
  \frametitle{Links}

  \alert{Python for Power System Analysis (PyPSA)}: \\
  \hspace{.5cm}a free software
  toolbox for simulating and optimising modern power systems

  \begin{itemize}
  \item \alert{Documentation} and \alert{examples} showcasing open data:   \url{https://pypsa.org/}
   \item \alert{Github}: \url{https://github.com/FRESNA/PyPSA}
   \item   \alert{Mailing list}: \url{https://groups.google.com/forum/\#!forum/pypsa}
  \item \alert{Research paper description}: \url{https://arxiv.org/abs/1707.09913}
  \end{itemize}
\end{frame}


\begin{frame}{Copyright}


  Unless otherwise stated, the graphics and text are Copyright \copyright Tom Brown, 2017.


  The graphics and text for which no other attribution are given are licensed under a
  \href{https://creativecommons.org/licenses/by/4.0/}{Creative Commons
  Attribution 4.0 International Licence}.

  \begin{center}\ccby\end{center}

\end{frame}

\end{document}
