\newcommand{\thistitle}{Lecture 7: Investment in Electricity Generation}

\input{title.tex}


\section{Introduction}



\begin{frame}
  \frametitle{Electricity investment: questions}

  \begin{itemize}
    \item When should generation companies invest in new generation capacity?
    \item How do generators make back their fixed costs from the market?
    \item Which technologies should generation companies invest in?
    \item Which technologies should society invest in?
    \item What is the most efficient combination of technologies in the long-run?
    \item How does CO$_2$ pricing affect this picture?
    \item How do variable renewables fit into this picture?
  \end{itemize}
\end{frame}



\begin{frame}
  \frametitle{National yearly load curve}

  Recall the Germany load curve (around 500 TWh/a) plotted hourly through the year.

  \centering
  \includegraphics[width=13cm]{DE-load-H}

\end{frame}



\begin{frame}
  \frametitle{Load duration curve}

  For some analysis it is useful to construct a \alert{duration curve}
  by stacking the hourly values from highest to lowest. This gives us the \alert{load duration curve}.

  \centering
  \includegraphics[width=13cm]{DE-load-duration}

\end{frame}




\begin{frame}
  \frametitle{Duration curve for generation}

  It can be useful to also see which technologies supply the load (here for a daily snapshot).

  But how do we determine their capacities?

  \centering
  \includegraphics[height=6.5cm]{load_curve_to_duration_curve.png}

\end{frame}





\begin{frame}
  \frametitle{Merit order recap}

\begin{columns}[T]
  \begin{column}{5cm}
    \begin{itemize}
      \item Recall that the \alert{market price} is set by the intersection of the demand curve with the supply curve.
        \item The supply curve is constructed from the \alert{merit order curve} by stacking up the marginal cost curves of the different plants.
\item In hours with high demand and low wind and solar production prices are high...
    \end{itemize}
  \end{column}
  \begin{column}{8cm}
  \includegraphics[width=8.5cm]{demand-supply-no_wind}
  \end{column}
\end{columns}
\end{frame}



\begin{frame}
  \frametitle{Merit order recap}

\begin{columns}[T]
  \begin{column}{4cm}

    \vspace{1cm}

    ...whereas in hours with low demand or high wind and solar production prices are high.

  \end{column}
  \begin{column}{8cm}
  \includegraphics[width=8.5cm]{demand-supply-with_wind}
  \end{column}
\end{columns}

\end{frame}

\begin{frame}
  \frametitle{Contribution margin}

\begin{columns}[T]
  \begin{column}{5cm}

    Recall that the \alert{contribution margin} is the selling price minus variable cost per unit, which is just price minus marginal cost for linear cost curves  $CM = p - MC$, i.e. the contribution towards covering the fixed costs.

    \vspace{.5cm}

    But what about the contribution margin in other hours?

  \end{column}
  \begin{column}{8cm}
    \begin{tikzpicture}[thick,scale=1.1]
    \begin{scope}[>={Stealth[black]}]
    \node[anchor=south west,inner sep=0] (image) at (0,0) {\includegraphics[width=8.5cm]{demand-supply-no_wind.pdf}};
    \draw[<->,black,line width=0.05cm] (1,0.8)--(1,3.9);
    \draw[right] (1,2.5) node{$CM_{\textrm{nuclear}}$};
    \draw[<->,black,line width=0.05cm] (2.7,1.1)--(2.7,3.9);
    \draw[right] (2.7,2.5) node{$CM_{\textrm{lignite}}$};
    \draw[<->,black,line width=0.05cm] (4.5,1.7)--(4.5,3.9);
    \draw[right] (4.5,2.5) node{$CM_{\textrm{hard coal}}$};
    \end{scope}
  \end{tikzpicture}
  \end{column}
\end{columns}
\end{frame}




\begin{frame}{Price curve}

  Consider the hourly prices over the full year (here from 2015):

  \centering
  \includegraphics[width=13cm]{price-2015}

\end{frame}

\begin{frame}{Price duration curve}

  By ordering we get a duration curve, the \alert{price duration curve}:

  \centering
  \includegraphics[width=13cm]{price-duration-2015}

\end{frame}



\begin{frame}
  \frametitle{Price duration curve}

  The price duration curve gives us the key link between variable costs, prices, capacity factor and the contribution margin.

  \centering
  \includegraphics[height=6.5cm]{price_duration-contribution_margin.png}

  \source{Erdmann et al, 2017}

\end{frame}


\begin{frame}{Multiple price duration}

  The optimal mix of generation is where, for each generation type,
  the area under the price–duration curve and above the variable cost
  of that generation type is equal to the fixed cost of adding
  capacity of that generation type.

  \centering
    \begin{tikzpicture}
\node[anchor=south west,inner sep=0] (image) at (0,0) {\includegraphics[width=8.5cm]{multiple-price-duration-clean}};
\draw (0.6,1.8) node{$o_1$};
\draw (0.6,2.6) node{$o_2$};
\draw (0.6,3.4) node{$o_3$};
  \end{tikzpicture}

  \source{Biggar and Hesamzadeh, 2014}
\end{frame}

\section{Screening curves for conventional generation}



\begin{frame}
  \frametitle{Levelised Cost Of Energy (LCOE)}

  Recall that the \alert{Levelised Cost Of Energy (LCOE)} in \euro/MWh was given by
  dividing the annualised cost (fixed and production-dependent
  variable costs) in \euro/a divided by the annual production $Q$ in MWh/a
  \begin{equation*}
    LCOE = \frac{1}{Q} \left( \frac{I_0}{PVF(r,T)} + B + oQ \right) = \frac{1}{Q} \left(I_0 \cdot a(r,T) + B  \right) + o
  \end{equation*}
  where $PVF(r,T)$ is the present value factor for a given WACC $r$
  and lifetime $T$, its inverse $a(r,T)$ is the annnuity, $B$ is the
  fixed operation and maintenance (FOM) cost and $o$ is the marginal
  cost (e.g. fuel and variable O\&M).

  The production $Q$ depends on the capacity of the generator $G$ and the \alert{capacity factor} $\theta \in [0,1]$ via
  \begin{equation*}
    Q = \theta \cdot 8760 \textrm{ h/a} \cdot G
  \end{equation*}
  (The capacity factor is related to the \alert{full load hours} FLH by FLH $= \frac{Q}{G} = \theta \cdot 8760$ h/a.)


\end{frame}



\begin{frame}
  \frametitle{From LCOE to annual cost per unit capacity}

  For generation investment analysis it is useful to take the LCOE
  \begin{equation*}
    LCOE = \frac{1}{Q} \left(I_0 \cdot a(r,T) + B  \right) + o
  \end{equation*}
  and multiply by the full load hours FLH $= \frac{Q}{G} = \theta \cdot 8760$ h/a to get the \alert{annual cost per unit capacity} $AC$ in \euro{}MW$^{-1}$a$^{-1}$
  \begin{equation*}
    AC = \frac{Q}{G} * LCOE = \frac{1}{G} \left(I_0 \cdot a(r,T) + B  \right) + o \frac{Q}{G} = i_0 \cdot a(r,T) + b + o\cdot\theta \cdot 8760
  \end{equation*}
  where $i_0 = \frac{I_0}{G}$ is the investment cost per capacity in \euro{}MW$^{-1}$ and $b = \frac{B}{G}$ is the FOM cost per capacity per year in \euro{}MW$^{-1}$a$^{-1}$.

\end{frame}

\begin{frame}[fragile]
  \frametitle{Parameters for different generation technologies}

  Here are some typical investment and operational parameters projected for 2020:
  \vspace{-.5cm}
  \begin{table}[!t]
	\centering
	\begin{tabular}{@{}lrrrrrrr@{}}
\toprule
Source   & Lifetime & Capital Cost &  Fix O\&{}M &  Var O\&{}M & $\eta$ & Fuel Cost & Marg. Cost \\
& years & \euro kW$^{-1}$  & \euro kW$^{-1}$a$^{-1}$ &  \euro MWh$_{\textrm{el}}^{-1}$ & [\%] & \euro/MWh$_{\textrm{th}}$ & \euro/MWh$_{\textrm{el}}$ \\
Symbol & $T$ & $i_0$ & $b$ & & & & $o$ \\
\midrule
Hard Coal    & 40 & 1200 & 30 & 6 & 39 & 10 & 32 \\
Gas OCGT     & 30 & 400  & 15 & 3 & 39 & 20 & 54 \\
Gas CCGT     & 30 & 800  & 20 & 4 & 60 & 20 & 37 \\
Nuclear      & 40-60 & 3000  & 0 & 6 & 33 & 3.3 & 16 \\
Wind Onshore & 25 & 1240 & 35 & 0 & & 0 & 0 \\
Solar PV     & 25 & 750  & 25 & 0 & & 0 & 0 \\
\bottomrule
	\end{tabular}
\end{table}

\source{\hrefc{https://www.diw.de/documents/publikationen/73/diw_01.c.424566.de/diw_datadoc_2013-068.pdf}{DIW Data Documentation, 2013}}
\end{frame}


\begin{frame}[fragile]
  \frametitle{Screening curve}
\begin{columns}[T]
  \begin{column}{6cm}
    A \alert{screening curve} plots the annual cost per capacity $AC$ in \euro{}kW$^{-1}$a$^{-1}$ of different technologies as a function of the FLH. Recalling that:
  \begin{equation*}
    AC(FLH) =  i_0 \cdot a(r,T) + b + o\cdot FLH
  \end{equation*}
  The y-axis-intercept is given by the fixed costs $i_0 \cdot a(r,T) + b$ while the slope is given by the variable cost $o$.

  From the screening curve we can read off which generation technology is lowest cost for a given FLH; more expensive technologies for that FLH are \alert{screened away}.

  \end{column}
  \begin{column}{7cm}
  \centering
  \includegraphics[width=8cm]{hirth-screening.png}
  \end{column}
\end{columns}

\source{\hrefc{http://www.open-electricity-economics.org/book/text/05.html}{Open Electricity Economics}}
\end{frame}


\begin{frame}[fragile]
  \frametitle{Screening curve analysis}

\begin{columns}[T]
  \begin{column}{5cm}

    To determine the optimal capacity mix we must:
    \begin{itemize}
    \item determine the crossing points in the screen curve, so we know for each FLH range what technology is cheapest
    \item map the FLH ranges from the screening curve to the FLH ranges in the load duration curve
    \item read off the generation capacities from the y-axis of the load duration curve
    \end{itemize}

  \end{column}
  \begin{column}{7cm}
  \centering
  \includegraphics[width=8.5cm]{chapter5_figure3.png}
  \end{column}
\end{columns}


  \source{\hrefc{http://www.open-electricity-economics.org/book/text/05.html}{Open Electricity Economics}}
\end{frame}

\begin{frame}[fragile]
  \frametitle{Power plants in the merit order}

  Different technologies have a different role in the merit order and screening curve analysis.

  \begin{table}[!t]
	\centering
	\begin{tabular}{@{}llp{2.3cm}llp{2cm}@{}}
          \toprule
          power plant type & FLH [h/a] & operation features & fixed costs & variable costs & examples \\
          \midrule
          \alert{baseload} & 7000+ & continuous & high & low & nuclear, lignite \\
          \alert{intermediate} & 4000-5000 & during peak hours (wd 8-8) & medium & medium & hard coal \\
          \alert{peaker} & $<$1500 & peak demand & low & high & gas, pumped-hydro storage \\
          \alert{load shedding} & 1-5 & yearly peak & none & v. high & load shedding \\
\bottomrule
	\end{tabular}
\end{table}

\end{frame}


\begin{frame}[fragile]
  \frametitle{What happens if fixed costs change?}

\begin{columns}[T]
  \begin{column}{5cm}

  Suppose nuclear fixed costs change, e.g. because of increased safety requirements.

    \begin{itemize}
    \item   Now the y-axis-intercept of nuclear is so high that there is no FLH for which nuclear is cheaper than the other technologies.
      \item  Nuclear is \alert{screened} away and doesn't appear on the optimal mix.
    \end{itemize}
  \end{column}
  \begin{column}{7cm}
  \centering
  \includegraphics[width=8.5cm]{chapter5_figure5.png}
  \end{column}
\end{columns}
  \source{\hrefc{http://www.open-electricity-economics.org/book/text/05.html}{Open Electricity Economics}}
\end{frame}


\begin{frame}[fragile]
  \frametitle{What happens if the CO$_2$ price increases?}

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

    Now suppose the CO$_2$ price is increased.

        \begin{itemize}
    \item     This increases the variable cost of each technology depending on its specific emissions (tCO$_2$/MWh\el).
\item    The slope for coal increases much more strongly than natural gas.
\item    As a result, coal is squeezed out of the optimal mix.
\item    The long-run effect of a CO$_2$ price is not just to decrease coal generation, but coal capacity too.
        \end{itemize}
  \end{column}
  \begin{column}{7cm}
  \centering
  \includegraphics[width=8cm]{chapter5_figure6.png}
  \end{column}
\end{columns}
  \source{\hrefc{http://www.open-electricity-economics.org/book/text/05.html}{Open Electricity Economics}}
\end{frame}


\section{Effect of variable renewables}

\begin{frame}[fragile]
  \frametitle{Integrating variable renewables into the screening curve analysis}


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

    Renewables cannot be dispatched at any time, so do not fit into the screening curve analysis.

    The re-ordering of time for the duration curve doesn't take account when wind and solar are available.

    However, once we know the renewable capacity, we can fix it and examine how the rest of the system adapts to the \alert{residual load}, load minus wind and solar.

  \end{column}
  \begin{column}{7cm}
  \centering
  \includegraphics[width=8cm]{chapter5_figure7.png}
  \end{column}
\end{columns}
  \source{\hrefc{http://www.open-electricity-economics.org/book/text/05.html}{Open Electricity Economics}}
\end{frame}


\begin{frame}[fragile]
  \frametitle{Residual load duration curve}

  From the residual load we can build the \alert{residual load duration curve} (RLDC).
  \centering
  \includegraphics[width=8cm]{chapter5_figure8.png}

  \source{\hrefc{http://www.open-electricity-economics.org/book/text/05.html}{Open Electricity Economics}}
\end{frame}




\begin{frame}[fragile]
  \frametitle{Integrating variable renewables into the screening curve analysis}


\begin{columns}[T]
  \begin{column}{4cm}

    The shape of the residual load curve now alters the optimal technology mix, leading to less of all technologies.


  \end{column}
  \begin{column}{9cm}
  \centering
  \includegraphics[width=10cm]{chapter5_figure9.png}
  \end{column}
\end{columns}
  \source{\hrefc{http://www.open-electricity-economics.org/book/text/05.html}{Open Electricity Economics}}
\end{frame}


\begin{frame}[fragile]
  \frametitle{Integrating variable renewables into the screening curve analysis}


\begin{columns}[T]
  \begin{column}{4cm}


    For high shares of wind and solar, particularly baseload technologies are pushed out of the system.

  \end{column}
  \begin{column}{9cm}
  \centering
  \includegraphics[width=10cm]{chapter5_figure10.png}
  \end{column}
\end{columns}
  \source{\hrefc{http://www.open-electricity-economics.org/book/text/05.html}{Open Electricity Economics}}
\end{frame}

\begin{frame}[fragile]
  \frametitle{Need for hourly system analysis}

  In order to assess the need for variable renewables, dispatchable generation and storage, you need an \alert{optimisation model} that can see the consecutive hours of demand, wind and solar. In this example of a low-CO$_2$ UK power system, excess wind is either stored as hydrogen or curtailed. Interested in more? Come to \alert{Energy Systems} course in Summer Semester!

  \centering
  \includegraphics[height=5.7cm]{GB-0}

\end{frame}

\section{Scarcity pricing and missing money problem}


\begin{frame}[fragile]
  \frametitle{How do peaking plants recover their costs?}

\begin{columns}[T]
  \begin{column}{5cm}

    If there is enough capacity to cover all demand situations, then the highest price in the system will be set by the variable cost of the peaking plant, e.g. natural gas.

    \vspace{.5cm}

    But how do peakers recover their fixed costs?

    \vspace{.5cm}

    This is the \alert{missing money problem}.
  \end{column}
  \begin{column}{7cm}
  \centering
  \includegraphics[width=8.5cm]{chapter5_figure3.png}
  \end{column}
\end{columns}


  \source{\hrefc{http://www.open-electricity-economics.org/book/text/05.html}{Open Electricity Economics}}
\end{frame}



\begin{frame}[fragile]
  \frametitle{Load shedding}

\begin{columns}[T]
  \begin{column}{5cm}

    \vspace{1cm}

    A solution is to allow some demand not to be met, i.e. \alert{load-shedding} costed at the \alert{value of lost load} (VOLL) which is typically very high (thousands of \euro/MWh).

    During these hours the price jumps to the VOLL, so that even the peakers recover their money.

  \end{column}
  \begin{column}{7cm}
  \centering
  \includegraphics[height=7.5cm]{chapter5_figure13-cropped.png}
  \end{column}
\end{columns}


  \source{\hrefc{http://www.open-electricity-economics.org/book/text/05.html}{Open Electricity Economics}}
\end{frame}



\begin{frame}[fragile]
  \frametitle{Load shedding}

\begin{columns}[T]
  \begin{column}{5cm}

    \vspace{1cm}

    A solution is to allow some demand not to be met, i.e. \alert{load-shedding} costed at the \alert{value of lost load} (VOLL) which is typically very high (thousands of \euro/MWh).

    During these hours the price jumps to the VOLL, so that even the peakers recover their money.

  \end{column}
  \begin{column}{7cm}
  \centering
  \includegraphics[height=7.5cm]{chapter5_figure13-cropped2.png}
  \end{column}
\end{columns}


  \source{\hrefc{http://www.open-electricity-economics.org/book/text/05.html}{Open Electricity Economics}}
\end{frame}


\begin{frame}{Episodes of High Prices are an Essential Part of an Energy-Only Market}

  In an energy-only market (in which generators are only compensated
  for the energy they produce), the wholesale spot price must at times
  be higher than the variable cost of the highest-variable-cost
  generating unit in the market. Episodes of high prices and/ or price
  spikes are not in themselves evidence of market power or evidence of
  market failure.

  However, there may be political or administrative restrictions on
  prices going to very high levels (i.e. consumer protection, concerns about market abuse).




\end{frame}


\begin{frame}{Last decade's market did not have episodes of very high prices}

  This made it hard for e.g. gas generators to make back their
  costs. Day ahead spot market prices in 2016 in Germany-Austria bidding zone:

  \centering
  \includegraphics[width=8cm]{germany-2016-price-duration}

  \raggedright
  Gas generators can bid into other markets, such as the intra-day or
  reserve power markets, or provide redispatch services.



\end{frame}


\begin{frame}{Market prices from highly renewable simulations}

  In our simulations for high renewable penetrations (taken from \href{https://arxiv.org/abs/1704.05492}{\bf\color{blue}\underline{this paper}}), the theory does
  however work:

  \centering
  \includegraphics[width=8.5cm]{benefits-lmp-lvopt.pdf}
  %data from https://zenodo.org/record/804338
  %supplementary_data_benefits_of_cooperation/results/
  %diw2030-CO0-T1_8761-wWsgrpHb-LVNone_c0_base_diw2030_solar1_7_angles_N1_5-2017-02-22-17-08-45/buses-marginal_price.csv

  \raggedright
  Prices are zero around a quarter of the time, but spike above 10,000 \euro/MWh in some hours.

\end{frame}

\begin{frame}{Price cap}

  Some markets implement a maximum market price cap (MPC), which may be below the Value of Lost Load (VoLL)
  ($V$ for the inelastic case).

  In the Eastern Australian National Electricity Market (NEM), a MPC
  of A\$15,000/MWh (\euro~9,300/MWh) for the 2020-2021 financial year
  is set, corresponding to the price automatically triggered when AEMO
  directs network service providers to interrupt customer supply in
  order to keep supply and demand in the system in balance.

  \centering

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



  \includegraphics[width=6.5cm]{price-cap}
\end{column}
\begin{column}{5cm}

  The Electric Reliability Council of Texas (ERCOT) has an energy only market with an MPC of \$9000/MWh.

  \vspace{.5cm}

  MPC can introduce distortions which make it difficult for some generators to recover costs.

\end{column}

\end{columns}


  \source{Biggar and Hesamzadeh, 2014}
\end{frame}



\begin{frame}{Capacity Remuneration Mechanisms vary widely}

  Capacity Remuneration Mechanisms (CRM) in 2019 in Europe and the US:

  \centering
  \includegraphics[height=6.8cm]{cpm-bublitz-2019.jpg}


  \source{\href{https://doi.org/10.1016/j.eneco.2019.01.030}{Bublitz et al, 2019}}

\end{frame}

\end{document}