\newcommand{\thistitle}{Lecture 14: Research Topics}

\input{title.tex}


\section{The World is Not a Perfect Optimization Model}


\begin{frame}
  \frametitle{We should be skeptical about models and modellers}
\begin{columns}[T]
  \begin{column}{7.5cm}

    \vspace{.2cm}
    \centering
    \includegraphics[width=7cm]{2019-01-10-IEEFA-EIA-coal-all-consumption-forecasts-470-x-395-v2-768x646}
  \end{column}
  \begin{column}{7.5cm}

    \vspace{.2cm}
    \centering
    \includegraphics[width=7cm]{auke.jpg}
  \end{column}
\end{columns}
\end{frame}

\begin{frame}
  \frametitle{We should be skeptical about models and modellers}

\begin{columns}[T]
  \begin{column}{9cm}

    \vspace{.2cm}
    \centering
    \includegraphics[width=9.5cm]{hubbert.png}
  \end{column}
  \begin{column}{5cm}

    \vspace{.2cm}
    \begin{itemize}
    \item Possible scenario projected from 1956 by US geologist M. King Hubbert
    \item Oil production in the US did indeed peak in the 1970s, but returned to peak height in last decade thanks to shale oil extraction with fracking
    \item Nuclear expanded but plateaued
      \item \alert{What might we be getting wrong in the 2020s?}
    \end{itemize}
  \end{column}
\end{columns}

\source{\hrefc{http://www.energycrisis.com/Hubbert/1956/1956.pdf}{Hubbert, 1956}}
\end{frame}


\begin{frame}
  \frametitle{We should be skeptical about models and modellers}

  Models can:
  \vspace{-.3cm}
    \begin{itemize}
    \item \alert{under- or overestimate rates of change} (e.g. under: PV uptake, over: onshore wind in UK/Germany/Netherlands)
    \item \alert{underestimate social factors} (e.g. concern about nuclear / transmission / wind)
    \item \alert{extrapolate based on uncertain data} (e.g. oil reserves, learning curves for PV)
    \item \alert{focus on easy-to-solve rather than policy-relevant problems} (e.g. most research)
    \item \alert{neglect uncertainty} (e.g. in short-term due to weather forecasts, or in long-term due to cost, political uncertainty and technological development)
    \item \alert{neglect need for robustness} (e.g. securing energy system against contingencies, attack)
    \item \alert{neglect complex interactions of markets and incentive structures} (e.g. abuse of market power, non-linearities not represented in models, lumpiness, etc.)
    \item \alert{neglect non-linearities and non-convexities} (e.g. power flow, or also learning curves, behavioural effects, perverse local optima, many, many more)
    \end{itemize}

\end{frame}

\begin{frame}
  \frametitle{Alternative modelling paradigms to optimisation}

  Not all models use optimisation. There are alternatives, such as:
  \begin{itemize}
  \item \alert{Simulation models} Advantages: can run efficiently, tend to be more transparent, can include more complicated effects. Disadvantages: no mathematical proof of optimality.
  \item \alert{Systems dynamics} Advantages: can capture long-run dynamics better, non-linear feedbacks. Disadvantages: potentially hard to parameterise, computation challenges.
  \item \alert{Agent-based modelling} Advantages: can do detailed parameterisation of social behaviour, can capture emergent effects. Disadvantages: only as good as the parameterisation, computation challenges.
  \end{itemize}

\end{frame}

\section{Robustness to Different Weather Years}


\begin{frame}
  \frametitle{Different Weather Years}

  Many of the simulations we looked at in this course, and many in the literature, used single weather years to determine optimal investments.

  This is problematic since:
  \begin{itemize}
  \item Weather changes from year to year
  \item There are decadal variations of wind
  \item Demand changes (particularly space heating demand during cold years)
  \end{itemize}

  But computing investments against 30 years of data (262,800 hours) is not feasible.

\end{frame}


\begin{frame}
  \frametitle{Different Weather Years}

  If we use different weather years to optimize sector-coupled European model with net-zero CO$_2$ emissions (including industry) we see broadly stable technology choices but variations in total system costs of up to 20\%.  NB: In real world cannot reoptimize investment every year!

  \centering
    \includegraphics[width=13cm]{lin-total_costs.png}

    \source{Lin Yang MA thesis}

\end{frame}


\begin{frame}
  \frametitle{Different Weather Years}

  Biggest changes are driven by space heating demand. Cold years (like 2010) are more expensive.

  \centering
    \includegraphics[width=14cm]{lin-heating.png}


    \source{Lin Yang MA thesis}

\end{frame}


\begin{frame}
  \frametitle{Different Weather Years}

  Optimal technology investments do not change dramatically from year to year. Here we show the mean capacities with standard deviation.

  \centering
    \includegraphics[width=14cm]{lin-generators.png}


    \source{Lin Yang MA thesis}

\end{frame}


\begin{frame}
  \frametitle{Different Weather Years}

  If we fix the optimal technology investments based on the weather of one year ($x$-axis), then run the dispatch over all 30 years (900 simulations in total), we can assess average curtailment and load-shedding. Using coldest year 2010 gives low load-shedding but high curtailment.

  \centering
    \includegraphics[width=14cm]{lin-run_30.png}

    \source{Lin Yang MA thesis}

\end{frame}


\begin{frame}
  \frametitle{Using 2010 investments}

  Using coldest year 2010 guarantees virtually no load-shedding in entire 30 years, but leads to excess energy in most years.
  Better to store excess energy from warmer years (e.g. chemically).

  \centering
    \includegraphics[width=14cm]{lin-use_2010.png}

    \source{Lin Yang MA thesis}

\end{frame}



\section{Effects of Climate Change on Energy System}


\begin{frame}
  \frametitle{Climate change}

  \begin{itemize}
  \item   What are the consequences of climate change for highly renewable energy systems?
  \item How will generation patterns for wind and solar change?
    \item What will be the effects on the dimensioning of wind,
      solar, storage, networks and backup generation?
  \end{itemize}

\end{frame}

\begin{frame}
  \frametitle{Climate change scenarios: RCP 8.5}

  Take a simulated dataset of how the weather would look
  between today and the year 2100 with a scenario of high
  concentrations of greenhouse gases.

  The scenario is called Representative Concentration Pathways 8.5
  (RCP~8.5), since it estimates a radiative forcing of $\Delta P = 8.5$~
  $\mathrm{W}/ \mathrm{m}^2$ (difference between insolation and energy
  radiated into space) at the end of the century. It is a \alert{worst-case scenario} and extrapolates current greenhouse gas emissions
  without reduction efforts (improbable given current trajectories of coal, renewables and EVs). This corresponds to a
  CO$_2$-equivalent-concentration (including all forcing agents) of
  approximately 1250 ppm (today around 410~pmm for CO$_2$) and an
  average temperature increase of $\Delta T = 3.7 \pm 1.1$~C at the
  end of the century, dependent on the model used.

  Compare historical values (HIS) to begin/middle/end of the century (B/M/EOC).

\end{frame}


\begin{frame}
  \frametitle{Changes to wind capacity factors}

  Left: historic (HIS) wind capacity factors 1970-2005

  Right: change at end of century (EOC) 2070-2100
  \begin{columns}[T]
    \begin{column}{9.5cm}

      \includegraphics[width=10cm]{cc-wind.png}
  \end{column}
  \begin{column}{4.5cm}
    \vspace{0.5cm}
    \begin{itemize}
    \item Small ($\sim 5\%$) average increase in Northern Europe
    \item Small ($\sim 5\%$) average decrease in Southern Europe
    \end{itemize}

  \end{column}
\end{columns}

      %corr_ensemble_sfcWind_abs.eps

  \source{\hrefc{https://arxiv.org/abs/1805.11673}{Schlott et al, 2018}}

\end{frame}


\begin{frame}
  \frametitle{Changes to solar capacity factors}

  \begin{columns}[T]
  \begin{column}{9.5cm}
    \includegraphics[width=10cm]{cc-solar.png}
  \end{column}
  \begin{column}{4.5cm}
    \vspace{0.5cm}
    \begin{itemize}
    \item Small ($\sim 5\%$) increase in
      in Southern Europe around Mediterranean
    \item Smallish ($\sim 10\%$) decrease in Northern Europe (due to
      increased cloud cover)
    \item Solar results known to be a little unreliable because of
      cloud modelling etc.
    \end{itemize}

  \end{column}
\end{columns}


    %mean_ensemble_sfcWind_abs.eps
      %corr_ensemble_sfcWind_abs.eps


  \source{\hrefc{https://arxiv.org/abs/1805.11673}{Schlott et al, 2018}}

\end{frame}

\begin{frame}
  \frametitle{Correlation Length}


  \begin{columns}[T]
  \begin{column}{5.5cm}
    \includegraphics[height=7.5cm]{simeon-correlation}
  \end{column}
  \begin{column}{8.5cm}
    The Pearson correlation coefficient of wind time series with a point in
        northern Germany decays exponentially with distance.
    Determine the \alert{correlation length} $L$ by fitting the
        function:
        \begin{equation*}
          \rho \sim e^{-\frac{x}{L}}
        \end{equation*}
        to the radial decay with distance $x$.

        \vspace{.2cm}
  \centering
    \includegraphics[height=4.5cm]{correlation_length.png}



  \end{column}
\end{columns}


  \source{\hrefc{https://doi.org/10.1016/j.apenergy.2011.10.039}{Hagspiel et al, 2012}}
\end{frame}


\begin{frame}
  \frametitle{Changes to wind speed correlation lengths}

  \begin{columns}[T]
  \begin{column}{9.5cm}
    \includegraphics[width=10cm]{cc-correlation.png}
  \end{column}
  \begin{column}{5.3cm}
    \begin{itemize}
      \item Correlation lengths are longer in the North than
        the South because of big weather systems that roll in from
        the Atlantic to the North (in the South they get dissipated).
      \item With global warming, correlation lengths grow
        longer in the North and shorter in the South.
      \item This is because weather systems have more energy and are
        bigger in the North.
    \end{itemize}

  \end{column}
\end{columns}


  \source{\hrefc{https://arxiv.org/abs/1805.11673}{Schlott et al, 2018}}

\end{frame}



\begin{frame}
  \frametitle{Effects of climate change on power system}

  Conclusions from study of effects on the power system:

    \begin{itemize}
    \item Most effects are small ($\sim 5-10\%$); total system costs increase by only 5\%.
     \item Longer correlation lengths see greater benefit from continental transmission.
     \item Impact of climate change is of a similar magnitude to the uncertainty between the different weather models.
       \item Not considered: Space heating and cooling demand changes may have bigger effect on overall energy system.
       \item Not considered: Impact of extreme weather events (storms, fires, droughts).
    \end{itemize}

    For more results, see `The Impact of Climate Change on a Cost-Optimal Highly Renewable European Electricity Network,' \urlc{https://arxiv.org/abs/1805.11673}

\end{frame}



%\section{Myopic Foresight for Weather Uncertainty}

%\section{Myopic Foresight for Multi-Decade Investment}

\section{Cost and Political Uncertainty}

\begin{frame}
  \frametitle{Power System Model: Sensitivity to Changing Solar Cost}

  In 30-node European electricity system with 95\% CO$_2$ reduction, change solar
  capital cost relative to default. NB: Even at zero solar cost, there
  is still wind. Why? Seasonality.\\
  LV 0: No cross-border grid, LV 125: compromise grid, LV Opt: optimal grid.

\centering
    \includegraphics[width=11cm]{sensitivity-solar_cost.png}

    \source{\hrefc{https://arxiv.org/abs/1803.09711}{Schlachtberger et al, 2018}}
\end{frame}



\begin{frame}
  \frametitle{Power System Model: Sensitivity to Onshore Wind Installable Potential}

  In electricity system with 95\% CO$_2$ reduction, reduce installable
  potential for onshore wind. Onshore substituted with offshore at only small
  extra system cost. BUT assumes sufficient grid capacity within each country to get offshore from coast to load.

\centering
    \includegraphics[width=11cm]{sensitivity-onshore_wind.png}

    \source{\hrefc{https://arxiv.org/abs/1803.09711}{Schlachtberger et al, 2018}}
\end{frame}


\begin{frame}
  \frametitle{Sensitivity of Optimisation to Cost, Weather Data and Policy Constraints}

  See Schlachtberger et al, `Cost optimal scenarios of a future highly renewable European
  electricity system: Exploring the influence of weather data, cost
  parameters and policy constraints,' 2018,
  \urlc{https://arxiv.org/abs/1803.09711}

\end{frame}


\section{Effect of Spatial Scale on Results of Energy System Optimisations}




\begin{frame}{Motivation: Transmission bottlenecks}

  Many of the results we've examined so far have aggregated countries
  to a single node. However, there are also transmission network
  bottlenecks \alert{within} countries (e.g. North to South Germany).


\centering
\includegraphics[width=8cm]{europe-transmission}
\source{ENTSO-E}


\end{frame}




\begin{frame}{Motivation: Wind and solar resource variation}

  There is also considerable variation in wind and solar resources...

    \begin{columns}[T]
\begin{column}{5cm}
  \includegraphics[trim=0 0cm 0 0cm,width=4.7cm,clip=true]{SolarGIS-Solar-map-Germany-de}
\end{column}
\begin{column}{6cm}
  \vspace{.3cm}
  \includegraphics[trim=0 0cm 0 0cm,width=6cm,clip=true]{43_Mittlere_Windgeschwindigkeit_100_m_Deutschland}
\end{column}
    \end{columns}

\end{frame}





\begin{frame}
  \frametitle{Spatial resolution}

\begin{columns}
\begin{column}{7cm}
We need spatial resolution to:
\begin{itemize}
\item capture the \alert{geographical variation} of renewables resources and the load
\item capture \alert{spatio-temporal effects} (e.g. size of wind correlations across the continent)
\item represent important \alert{transmission constraints}
\end{itemize}

BUT we do not want to have to model all 5,000 network nodes of the European system.
\end{column}
\begin{column}{6cm}
\centering
% No, we really do not not want to optimise a model of 4653 substation, 5613 AC lines and 26 DC lines of the European HV electricity network.
\includegraphics[width=6.5cm]{pre-2-network-full.pdf}
\source{Own representation of Bart Wiegman's GridKit extract of the
  online ENTSO-E map, \url{https://doi.org/10.5281/zenodo.55853}}
\end{column}
\end{columns}
\end{frame}

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

  There are lots of algorithms for clustering 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{$k$-means clustering on load \& conventional generation}

  Our \alert{goal}: maintain main transmission corridors of today to
  investigate highly renewable scenarios with no grid expansion. Since generation fleet is totally rebuilt, do not want to rely on current generation dispatch (like e.g. LMP algorithm).

  Today's grid was laid out to connect big generators and load centres.

  \begin{columns}

    \begin{column}{5cm}

      \vspace{0.5cm}
  \alert{Solution}:
  Cluster nodes based on spatial distribution using $k$-means, with a weighting to sites with higher average load and conventional generation capacity.
    \end{column}

    \begin{column}{7cm}
      \vspace{.3cm}
            \includegraphics[width=6.5cm]{clustering.pdf}
    \end{column}
\end{columns}
\end{frame}

\begin{frame}
  \frametitle{$k$-means clustering on load \& conventional generation}

  Suppose the $N$ nodes $i$ have spatial coordinates $(x_i,y_i)$. The $k$-means algorithm works by partitioning them into $k\leq N$ sets $N_c$ for $c = 1, \dots k$ such that the sum of squared distance to the centroid $(x_c,y_c)$ (mean point inside each set) is minimised:
  \begin{equation*}
    \min_{\{(x_c,y_c)\}} \sum_{c=1}^k \sum_{i \in N_c} w_i \left|\left| \left(\begin{matrix}
      x_c \\
      y_c
\end{matrix}\right) -  \left(\begin{matrix}
      x_i \\
      y_i
\end{matrix}\right)\right|\right|^2
  \end{equation*}
  Each node $i$ is weighted $w_i$ by the average load and the
  average conventional generation there.

  Use the centroid as the location of the new clustered node.
\end{frame}



\begin{frame}
  \frametitle{Reconstitution of network}

  Once the partition of nodes is determined:
  \begin{itemize}
  \item A new node is created to represent each set of clustered nodes
  \item Hydro capacities and load is aggregated at the node; VRE (wind and solar) time series are aggregated, weighted by capacity factor; potentials for VRE aggregated
  \item Lines between clusters replaced by single line with length 1.25 $\times$ crow-flies-distance, capacity and impedance according to replaced lines
    \item $n-1$ blanket safety margin factor grows from 0.3 with $\geq 200$ nodes to 0.5 with 37 nodes (to account for aggregation)
  \end{itemize}

\end{frame}

\begin{frame}
  \frametitle{$k$-means clustering: Networks}

\centering
 \includegraphics[width=13cm]{networks-clustered-crop}
  % $\vcenter{\hbox{\includegraphics[width=4cm]{pre-2-network-full}}}$
  % $\vcenter{\hbox{\includegraphics[width=4cm]{pre-2-network-362-LV-1}}}$
  % $\vcenter{\hbox{\includegraphics[width=4cm]{pre-2-network-181-LV-1}}}$ \\
  % $\vcenter{\hbox{\includegraphics[width=4cm]{pre-2-network-128-LV-1}}}$
  % $\vcenter{\hbox{\includegraphics[width=4cm]{pre-2-network-64-LV-1}}}$
  % $\vcenter{\hbox{\includegraphics[width=4cm]{pre-2-network-37-LV-1}}}$



\end{frame}



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

  How is the overall minimum of the cost objective (building and
  running the electricity system) affected by an increase of spatial
  resolution in each country?

  We expect
  \begin{itemize}
  \item A better representation of existing internal bottlenecks will prevent the transport of e.g. offshore wind to the South of Germany.
  \item Localised areas of e.g. 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 energy shares 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}

  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{Costs: Focus on Germany (w/o grid expansion)}

\begin{columns}[T]
\begin{column}{8.5cm}
\centering
  \includegraphics[width=8.5cm]{cost_de_breakdown-1-0}
  %\includegraphics[width=6cm]{pre-2-costs_de_storage}
\end{column}
\begin{column}{6cm}
  \begin{itemize}
  \item Offshore wind replaced by onshore wind at better sites and solar (plus batteries), since
  the represented transmission bottlenecks make it impossible to
  transport the wind energy away from the coast
  \item the effective onshore wind capacity factors increase from $26\%$ to up to $42\%$
  \item Investments stable at 181 clusters and above
  \end{itemize}
\end{column}
\end{columns}


\end{frame}




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

  6 different scenarios of network expansion by constraining the
  overall transmission line volume in relation to today's line volume $\mathrm{CAP}_{\mathrm{trans}}^{\mathrm{today}}$, given length $d_\ell$ and capacity
  $F_\ell$ of each line $\ell$:
  \begin{align}
    F_\ell & \geq F_\ell^{\mathrm{today}} \\
    \sum_\ell d_\ell F_\ell & \leq \mathrm{CAP}_{\mathrm{trans}}
  \end{align}
  where
  \begin{equation}
    \mathrm{CAP}_{\mathrm{trans}} = x \, \mathrm{CAP}_{\mathrm{trans}}^{\mathrm{today}}
  \end{equation}

  for $x = 1$ (today's grid) $x = 1.125,1.25,1.5,2$, $x=3$ (optimal for overhead line at high number of cluster).
\end{frame}





\begin{frame}
  \frametitle{With 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-1-5-256.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}
  \includegraphics[width=9.5cm]{cost_eu}

\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{Costs: Focus on Germany (CAP = 3)}

\begin{columns}[T]
\begin{column}{8.5cm}
\centering
  \includegraphics[width=8.5cm]{cost_de_breakdown-3-0}
  %\includegraphics[width=6cm]{pre-2-costs_de_storage}
\end{column}
\begin{column}{6cm}
  \begin{itemize}
  \item Investment reasonably stable at 128 clusters and above
  \item System consistently dominated by wind
  \item No solar or battery for any number of clusters
  \end{itemize}
\end{column}
\end{columns}


\end{frame}




\begin{frame}
  \frametitle{Behaviour as CAP is changed}


\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 Same non-linear development with high number of nodes that we saw with one node per country
      \item Most of cost reduction happens with small expansion; cost
        rather flat once capacity has doubled, reaching minimum (for
        overhead lines) at 3 times today's capacities
      \item Solar and batteries decrease significantly as grid expanded
  \item  Reduction in storage losses too
  \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{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{CO2 prices versus line cap for 181 clusters}



\begin{columns}[T]
\begin{column}{10cm}
\centering
  \includegraphics[width=11cm]{shadows-co2}
  %\includegraphics[width=6cm]{pre-2-costs_de_storage}
\end{column}
\begin{column}{4cm}
  \begin{itemize}
    \vspace{2cm}
%\item   %Big reduction in curtailment
  \item CO2 price of between 150 and 250 \euro/tCO2 required to reach these solutions, depending on line volume cap
  \end{itemize}
\end{column}
\end{columns}

\end{frame}




% \begin{frame}
%   \frametitle{Comparison of results: energy}

% \centering

%   \includegraphics[width=4.5cm]{pre-2-clusters-yearly_energy-LV-inf}
%   \includegraphics[width=4.5cm]{pre-2-clusters-yearly_energy-LV-4}
%   \includegraphics[width=4.5cm]{pre-2-clusters-yearly_energy-LV-1}

% \end{frame}


% \section{Conclusions}



\begin{frame}
  \frametitle{More Details in Paper}

  For more details, see the following paper:
  \begin{itemize}
  \item J. Hörsch, T. Brown, ``The role of spatial scale in joint optimisations of generation and transmission for European highly renewable scenarios,'' EEM 2017, \href{https://arxiv.org/abs/1705.07617}{\bf\color{blue}\underline{link}}.
  \end{itemize}

  In an upcoming paper with Martha Frysztacki and the same authors, we disentangle the effects of the network resolution from the renewable resource resolution.

\end{frame}


\begin{frame}
  \frametitle{Conclusions}

  \begin{itemize}
    \item Generation costs always dominate grid costs, but the grid can cause higher generation costs if expansion is restricted
    \item Systems with no grid extension beyond today are up to 25\% more expensive, but small grid extensions (e.g. 25\% more capacity than today) can lock in big savings
    \item Need at least around 200 clusters for Europe to see grid bottlenecks if no expansion
    \item Can get away with $\sim 120$ clusters for Europe if grid expansion is allowed
    \item This is \alert{no single solution} for highly renewable systems, but a \alert{family of solutions}  with different costs and compromises
    \item Much of the stationary storage needs can be eliminated by sector-coupling: DSM with electric vehicles, thermal storage; this makes grid expansion less beneficial
    \item Understanding the need for \alert{flexibility at different temporal and spatial scales} is key to mastering the complex interactions in the energy system
  \end{itemize}
\end{frame}


\section{Near-Optimal Energy Systems}

\begin{frame}
  \frametitle{Flat directions near optimum}

  Both for changing transmission expansion AND onshore wind installable potentials, we've seen that total system costs are \alert{flat around the optimum}.

  Can we explore this \alert{near-optimal space} more systematically?

  \vspace{.5cm}
\begin{columns}[T]

  \begin{column}{6cm}
  \includegraphics[width=6cm]{costs_per_cluster_181}
  \end{column}
  \begin{column}{8cm}
    \includegraphics[width=8cm]{sensitivity-onshore_wind.png}
  \end{column}
\end{columns}

\end{frame}
% optimal
\begin{frame}
  \frametitle{Large Space of Near-Optimal Energy Systems}

  There is a \alert{large degeneracy} of different possible energy systems close to the optimum.

  \vspace{.2cm}
  \centering
  \includegraphics[page=2, trim=0.3cm 16.02cm 0cm 3.05cm, clip, height=0.83\textheight]{sketch.pdf}
  \source{Fabian Neumann}
\end{frame}

% epsilon constraint
\begin{frame}
  \frametitle{Large Space of Near-Optimal Energy Systems}

  Consider the part of the feasible space within $\varepsilon$ of the optimum $f(x^*)$.

  \vspace{.2cm}
  \centering
  \includegraphics[page=1, trim=0.3cm 0.7cm 0cm 18.35cm, clip, height=0.83\textheight]{sketch.pdf}
  \source{Fabian Neumann}
\end{frame}

% mga
\begin{frame}
  \frametitle{Large Space of Near-Optimal Energy Systems}

  Now within $\varepsilon$ of the optimum $f(x^*)$, try minimising or maximising $x$, to probe space.

  \vspace{.2cm}
  \centering
  \includegraphics[page=1, trim=0.3cm 15.45cm 0cm 3.6cm, clip, height=0.83\textheight]{sketch.pdf}
  \source{Fabian Neumann}
\end{frame}



% 2-dimensional
\begin{frame}
  \frametitle{Large Space of Near-Optimal Energy Systems}

  NB: Decision space of variables is multi-dimensional, so can probe only one direction at a time.

  \vspace{.2cm}
  \centering
  \includegraphics[page=1, trim=8.8cm 11.5cm 9.4cm 14.8cm, clip, height=0.83\textheight]{sketch.pdf}
  \source{Fabian Neumann}
\end{frame}



\begin{frame}{Application: Highly-Renewable European Electricity System}

  Apply this technique to a 100-node model of the European electricity with 100\% renewable energy.
  \begin{enumerate}
    \item Find the \alert{least-cost power system}.
    ~\\
    \item For $\varepsilon\in\{0.5,1,\dots,10\} \%$ \alert{minimise/maximise} investment in
    \begin{itemize}
      \item generation capacity {(onshore and/or offshore wind, solar)},
      \item storage capacity {(hydrogen, batteries, total storage)} and
      \item transmission volume {(HVAC lines and HVDC links)}
    \end{itemize}
    such that \alert{total annual system costs increase by less than $\varepsilon$}.
  \end{enumerate}

  \vspace{.5cm}
  Methodology adapted from Method to Generate Alternatives (MGA) but `alternatives' are forced in politically-interesting directions.

  \source{Fabian Neumann}

\end{frame}



\begin{frame}
  \frametitle{Example: 100\% renewable electricity system for Europe}

\begin{columns}[T]
  \begin{column}{7cm}
    Capacity expansion in optimum:

    \includegraphics[width=7cm]{no-optimum.png}
  \end{column}
  \begin{column}{7cm}

    $\varepsilon =$ 10\% above optimum, minimise new grid:

    \includegraphics[width=7cm]{no-trans-10.png}
  \end{column}
\end{columns}



  \source{\hrefc{https://arxiv.org/abs/1910.01891}{Neumann \& Brown, 2020}}

\end{frame}


\begin{frame}
  \frametitle{Example: 100\% renewable electricity system for Europe}

\begin{columns}[T]
  \begin{column}{7cm}
    \includegraphics[trim=0cm 0cm 0cm 0cm, clip, width=7cm]{space-00.pdf}
  \end{column}
  \begin{column}{6.5cm}

    Within 10\% of the optimum we can:
    \begin{itemize}
    \item Eliminate most grid expansion
    \item Exclude onshore or offshore wind or PV
    \item Exclude battery or most hydrogen storage
    \end{itemize}

    \vspace{.2cm}

    \alert{Robust conclusions}: wind, some transmission, some storage, preferably hydrogen storage, required for a cost-effective solution.

    \vspace{.2cm}

    This gives space to choose solutions with \alert{higher public acceptance}.
  \end{column}
\end{columns}


  \source{\hrefc{https://arxiv.org/abs/1910.01891}{Neumann \& Brown, 2020}}

\end{frame}



\begin{frame}[fragile]
  \frametitle{Flat directions allow society to choose based on other criteria}



\begin{columns}[T]

  \begin{column}{5cm}


\centering
\includegraphics[width=5cm]{nein_zur_monstertrasse}

  \end{column}


  \begin{column}{6.7cm}

    \vspace{.5cm}

    This flatness may allow us to choose solutions with \alert{higher
      public acceptance} at only \alert{small extra cost}.

    \vspace{.5cm}

    These trade-offs will occupy us for the next 30 years!

    \vspace{.5cm}

\includegraphics[width=7cm]{Protestplakat-gegen-den-Bau-von-Windraedern-in-Hamburg-Deutschland.jpg}

  \end{column}

\end{columns}

\end{frame}


\begin{frame}{\textbf{Dependencies:} Extremes cannot be achieved simultaneously}

  \begin{columns}

    \begin{column}{0.4\textwidth}
      \begin{center}
        \vspace{-0.5cm}
        \footnotesize Optimal System Layout\\
        \includegraphics[height=0.8\textheight]{capacity-bar.pdf}
      \end{center}
    \end{column}
    %\vrule
    \begin{column}{0.6\textwidth}
      \begin{center}
        \vspace{.3cm}
        \includegraphics[height=0.9\textheight]{capacity-bars.pdf}
      \end{center}
    \end{column}

  \end{columns}

\end{frame}

\begin{frame}
  \frametitle{Near-Optimal Systems: Conclusions}

  \begin{itemize}
  \item Optimizing a single model gives a \alert{false sense of exactness}.
  \item There are many uncertainties about cost assumptions and political targets.
  \item There are also \alert{structural model uncertainties} since the feasible space can be very \alert{flat} near the optimum, such that the solution chosen is random within flat area.
  \item We can use these techniques to probe the \alert{near-optimal space}.
  \item This gives us fuzzier but \alert{more robust} conclusions (e.g. need wind, some transmission and some long-term storage for a cost-effective solution).
    \item It also allows us to find cost-effective solutions with \alert{higher public acceptance}.

  \end{itemize}

  More details: Fabian Neumann, Tom Brown, ``The Near-Optimal Feasible Space of a Renewable Power System Model,'' 2020, EPSR, \urlc{https://arxiv.org/abs/1910.01891}.

\end{frame}
\end{document}