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\title{Electricity Markets: Summer Semester 2016, Lecture 7}
%\subtitle{---}
\author{
  Tom Brown, Mirko Schäfer
}

\institute{
  Frankfurt Institute of Advanced Studies (FIAS), Goethe-Universit\"at Frankfurt \\
  FIAS Renewable Energy System and Network Analysis (FRESNA) \\
  \\
  \url{{brown, schaefer}@fias.uni-frankfurt.de}
}


\date{30th May 2016}


\titlegraphic{%
  \vspace{7cm}
    \includegraphics[width=4cm]{FIAS-logo}
}

\begin{document}

\maketitle


\begin{frame}

  \frametitle{Table of Contents}
  \setbeamertemplate{section in toc}[sections numbered]
  \tableofcontents[hideallsubsections]
\end{frame}


\section{Duration Curves and Capacity Factors: Examples from Germany in 2015}

\begin{frame}{Load curve}

  Here's the electrical demand (load) in Germany in 2015:

  \centering
  \includegraphics[width=10.5cm]{load-2015}
  \raggedright

  To understand this curve better and its implications for the market,
  it's useful to stack the hours of the year from left to right in
  order of the amount of load.

\end{frame}


\begin{frame}{Load duration curve}

  This re-ordering is called a \alert{duration curve}.\\
  For the load it's the \alert{load duration curve}.

  \centering
  \includegraphics[width=10.5cm]{load-duration-2015}

\end{frame}

\begin{frame}{Nuclear curve}

  Can do the same for nuclear output:

  \centering
  \includegraphics[width=10.5cm]{Nuclear-2015}

\end{frame}

\begin{frame}{Nuclear duration curve}

  Duration curve is pretty flat, because it is economic to run nuclear almost all the time as  \alert{baseload plant}:

  \centering
  \includegraphics[width=10.5cm]{Nuclear-duration-2015}

  \raggedright
  The equivalent fraction of time that the plants run at full capacity over the year is the \alert{capacity factor} - nuclear has a high capacity factor, usually around 70-90\%.
\end{frame}


\begin{frame}{Gas curve}

  Can do the same for gas output:

  \centering
  \includegraphics[width=10.5cm]{Gas-2015}

\end{frame}

\begin{frame}{Gas duration curve}

  Duration curve is partially flat (for heat-driven CHP) and partially peaked (for \alert{peaking plant}):

  \centering
  \includegraphics[width=10.5cm]{Gas-duration-2015}

  \raggedright
  The capacity factor for gas is much lower - more like 20\%.
\end{frame}

\begin{frame}{Price curve}

  Can do the same for price during the year:

  \centering
  \includegraphics[width=10.5cm]{price-2015}

\end{frame}

\begin{frame}{Price duration curve}

  Price duration curve:

  \centering
  \includegraphics[width=10.5cm]{price-duration-2015}

\end{frame}



\begin{frame}{Question}



  Now we are in a position to consider the questions:

  \begin{itemize}
    \item What determines the distribution of investment in different generation technologies?
    \item How is it connected to variable costs, capital costs and capacity factors?
  \end{itemize}

  We will find the price and load duration curves very useful.
\end{frame}



\section{Long-run Efficiency: Optimal Investment in Generation with a Single Technology}

\begin{frame}{Definition of long-run efficiency}

  Up until now we have considered \alert{short-run} equilibria that
  ensure \alert{short-run} efficiency (static), i.e. they make the best use of
  presently available productive resources.

  \alert{Long-run} efficiency (dynamic) requires in addition the optimal
  investment in productive capacity.

  Concretely: given a set of options, costs and constraints for different
  generators (nuclear/gas/wind/solar) what is the optimal generation
  portfolio for maximising long-run welfare?

  From an indivdual generators' perspective: how best should I invest in extra capacity?

  We will show again that with perfect competition and no barriers to
  entry, the system-optimal situation can be reached by individuals
  following their own profit.

\end{frame}


\begin{frame}{Simple example: Single generator type with downward sloping demand}

  Consider the long-run efficiency from the total system perspective with a single generator
  type with linear cost function and downward-sloping demand (taken
  from Biggar-Hesamzadeh pages 21 and 183).

  We have to consider \alert{marginal costs} arising from each unit of
  production $Q$ and \alert{capital costs} that arise from fixed costs
  regardless of the rate of production (such as the investment in building
  capacity $K$).

  For a given production rate $Q$ and capacity $K$ we have in this simple example a cost
  \begin{equation*}
    C(Q,K) = cQ + fK
  \end{equation*}
  with $0 \leq Q \leq K$, where $C(Q,K)$ has units \euro/h, $c$ has units \euro/MWh, $Q$ and
  $K$ have units MW and $f$ has units \euro/MW/h (`hourised' capital
  cost).

  Note again: the term $fK$ is constant regardless of production rate $Q$.
\end{frame}


\begin{frame}{Can't just consider just one load situation}

  Up until now, in our considerations of short-run efficiency, we've
  considered just a \alert{single} demand situation.

  Now that we're considering long-term investment, we have to consider
  \alert{many} or even \alert{all} demand situations.


  \includegraphics[width=5cm]{downward_slope-single}
  \includegraphics[width=5cm]{downward_slope--600}

  We consider many different utility curves $U_t(Q)$ for different
  times $t$, each of which occurs with probability $p_t>0$, $\sum p_t =
  1$.

\end{frame}


\begin{frame}{Simple example: Consumer with downward sloping demand}

  Suppose the generators have a marginal cost of $c=$40
  \euro/MWh and the downward-sloping demand fluctuates over time.

  If total generation capacity is always below demand, the demand will
  set the price at MCB (Marginal Consumer Benefit) and the generators will always earn above their Marginal Generation Cost (MGC):

  \centering
  \includegraphics[width=6cm]{downward_slope600}

  But then why don't they build more capacity to make even more profit?

\end{frame}


\begin{frame}{Simple example: Consumer with downward sloping demand}

  If sometimes the price is set by MCB and sometimes by the MGC then the generators might still earn enough  to cover their capital costs:

    \centering
  \includegraphics[width=7cm]{downward_slope800}

\end{frame}

\begin{frame}{Simple example: Consumer with downward sloping demand}

  If generation capacity is so large that it can always cover the demand, regardless of the MCB, then generators will never earn enough money to regain their capital costs, because the price will always be set by the marginal generation cost:

    \centering
  \includegraphics[width=7cm]{downward_slope1000}

\end{frame}





\begin{frame}{Simple example: optimisation problem}

  Now consider the maximisation of long-run welfare, including the capital costs:
  \begin{equation*}
    \max_{\{Q^B_t\},\{Q^S_t\}, K} \sum_t p_t\left[ U_t(Q_t^B) - C(Q_t^S,K)\right]
  \end{equation*}
  i.e. with cost $C(Q,K) = cQ + fK$ we optimise
  \begin{equation*}
        \max_{\{Q^B_t\},\{Q^S_t\}, K} \sum_t p_t\left[ U_t(Q_t^B) - (cQ_t^S+fK)\right]
  \end{equation*}
  given
  \begin{align*}
    Q^B_t - Q^S_t =  0 \hspace{1cm}\leftrightarrow \hspace{1cm} p_t\l_t \hspace{1cm} \forall t \\
    -Q^S_t \leq 0 \hspace{1cm}\leftrightarrow \hspace{1cm} p_t\ubar{\mu}_t \hspace{1cm} \forall t \\
         Q^S_t \leq K \hspace{1cm}\leftrightarrow \hspace{1cm} p_t\bar{\mu}_t \hspace{1cm} \forall t
  \end{align*}
  (We have taken the liberty to multiply the KKT multipliers by a constant $p_t>0$, to make the resulting equations easier to read.)
\end{frame}



\begin{frame}{Simple example: KKT}

  From stationarity we get:
  \begin{align*}
    \frac{\d \cL}{\d Q_t^B} &\Rightarrow  p_tU_t' (Q_t^B) - p_t\lambda_t  = 0 \\
    \frac{\d \cL}{\d Q_t^S} &\Rightarrow  -p_t c+p_t\l_t +p_t\ubar{\m}_t - p_t\bar{\m}_t  = 0 \\
    \frac{\d \cL}{\d K} &\Rightarrow  -f+ \sum_t p_t\bar{\m}_t  = 0
  \end{align*}

  From primal feasibility we get $Q_t^B = Q_t^S = Q_t^*$ and from complementary slackness we have $\ubar{\m}_t^* = 0$, assuming the demand is always positive, and $\bar{\m}_t^* \geq 0$. Thus we get
  \begin{align*}
    \lambda_t^* & = U_t'(Q_t^*) \\
    \lambda_t^* & = c+\bar{\m}_t^* \\
    f & = \sum_t p_t \bar{\m}_t^*
  \end{align*}

\end{frame}



\begin{frame}{Simple example: KKT interpretation}

  We have
  \begin{align*}
    \lambda_t^* & = U_t'(Q_t^*) \\
    \lambda_t^* & = c+\bar{\m}_t^* \\
    f & = \sum_t p_t \bar{\m}_t^*
  \end{align*}

  So $\bar{\m}_t^*$ is the difference between the Marginal Generation Cost (MGC) $c$ and the Marginal Consumer Benefit (MCB) $U_t'(Q_t^*)$.

  If the constraint $Q_t \leq K$ is binding, then $\bar{\m}_t^* \geq 0$.

  The optimal investment level happens when the average value of $\bar{\m}_t^*$, $\sum_t p_t \bar{\m}_t^*$, is equal to the capital cost $f$.
\end{frame}




\begin{frame}{Downward Price Duration}


  \centering
  \includegraphics[width=10.5cm]{downward-price-duration}

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






\begin{frame}{Simplified case: inelastic demand}

  Now consider a simplified case where the demand is \alert{inelastic} with a very high Marginal Consumer Benefit of $V$, sometimes called the \alert{Value of Lost Load (VoLL)} i.e.
  \begin{equation*}
    U_t(Q_t) = \left\{ \begin{array}{ll}
      VQ_t & \textrm{ for } Q_t \leq \hat{Q}_t \\
      \frac{1}{2} V\hat{Q}_t^2 & \textrm{ for } Q_t > \hat{Q}_t
    \end{array}\right.
  \end{equation*}
  i.e.
  \begin{equation*}
    U_t'(Q_t) = \left\{ \begin{array}{ll}
      V& \textrm{ for } Q_t \leq \hat{Q}_t \\
      0 & \textrm{ for } Q_t > \hat{Q}_t
    \end{array}\right.
  \end{equation*}

  In this case the clearing price is binary: it is either set by the marginal generation cost $c$ for the case that demand is lower than generation capacity $\hat{Q}_t < K$ (where $\bar{\m} = 0$) or by the marginal consumer benefit $V$ if demand exceeds the generation capacity $\hat{Q}_t \geq K$ (where $\bar{\m} = V-c$).

  In this case
  \begin{equation*}
      f = P(\hat{Q}_t > K) (V-c)
  \end{equation*}

\end{frame}


\begin{frame}{Example of VoLL from New South Wales, Australia}

  VoLL depends on consumer:

  \includegraphics[width=10.5cm]{voll}

  (1 Australian \$ = 0.65 \euro)

  The average value of customer reliability is estimated at
  close to A\$95,000/MWh.

  \source{AEMC, 2012, via Jenny Riesz}

\end{frame}


\begin{frame}{Simplified case: inelastic demand}


  We can turn this around and define the \alert{loss of load probability (LOLP)} as the probability that voluntary load
  shedding will be required:
  \begin{equation*}
    LOLP(K) = P(\hat{Q}_t > K)  = \frac{f}{V-c}
  \end{equation*}

  In other words, it will not
  be efficient to choose a level of capacity that guarantees 100\% reliability (that is, the
  probability that load will be left unserved is not zero).

  In an optimal dispatch with inelastic demand up to some valuation $V$, at the
  optimal level of generation capacity, there will remain a finite probability that some load
  will be left unserved.
\end{frame}


\begin{frame}{Inelastic load duration curve}


  \centering
  \includegraphics[width=10.5cm]{inelastic-load-duration}

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




\section{Long-run Efficiency: Optimal Investment in Generation with Multiple Technologies}


\begin{frame}{Extension to multiple technologies}

  Now consider several different generation technologies $T$ each with different marginal and capital costs, with downward sloping demand.

  For a given production rate $Q_T$ and capacity $K_T$ we have for the linear case
  \begin{equation*}
    C(Q_T,K_T) = c_TQ_T + f_TK_T \textrm{  for  } 0 \leq Q_T \leq K_T
  \end{equation*}

  The maximisation of long-run welfare, including the capital costs, is:
  \begin{equation*}
    \max_{\{Q^B_t\},\{Q^S_{t,T}\},\{ K_T\}} \sum_t p_t\left[ U_t(Q_t^B) - \sum_T C_T(Q_{t,T}^S,K_T)\right]
  \end{equation*}
  given
  \begin{align*}
    Q^B_t - \sum_{T} Q^S_{t,T} =  0 \hspace{1cm}\leftrightarrow \hspace{1cm} p_t\l_t \hspace{1cm} \forall t \\
    -Q^S_{t,T} \leq 0 \hspace{1cm}\leftrightarrow \hspace{1cm} p_t\ubar{\mu}_{t,T} \hspace{1cm} \forall t,T \\
         Q^S_{t,T} \leq K_T \hspace{1cm}\leftrightarrow \hspace{1cm} p_t\bar{\mu}_{t,T} \hspace{1cm} \forall t,T
  \end{align*}

\end{frame}



\begin{frame}{Multiple example: KKT}

  From KKT we have for $Q_t^* = \sum_{T} Q_{t,T}^*$:
  \begin{align*}
    \frac{\d \cL}{\d Q_t^B} &\Rightarrow  U_t' (Q_{t}^*) = \lambda_t^*  \\
    \frac{\d \cL}{\d Q_{t,T}^S} &\Rightarrow  \l_t^* - c_T =  \bar{\m}_{t,T}^*   - \ubar{\m}_{t,T}^* \\
    \frac{\d \cL}{\d K_T} &\Rightarrow  f_T = \sum_t p_t\bar{\m}_{t,T}^*
  \end{align*}

  If $c_1 \leq c_2 \leq \cdots \leq c_N$ and $S_n = \sum_{i=1}^n K_i$
  then:

  If $\l_t^* \geq c_T$ we have $Q_{t,T}^* = K_T$,
  $\bar{\m}_{t,T}^* = \l_t^* - c_T$ and $\ubar{\m}_{t,T}^* = 0$.

  If $\l_t^* < c_T$ then $Q_{t,T}^* = 0$,
  $\bar{\m}_{t,T}^* = 0$ and $\ubar{\m}_{t,T}^* = c_T - \l_t^*$.


\end{frame}



\begin{frame}{Multiple example: KKT}

  $f_T = \sum_t p_t\bar{\m}_{t,T}^*$ becomes
  \begin{equation*}
    f_T = \sum_{t \textrm{ s.t. } \l_t^* \geq c_T} p_t (\l_t^* - c_T)
  \end{equation*}

  i.e.
  \begin{equation*}
    \mathbb{E}(\l | \l \geq c_T) = c_T + \frac{f_T}{P(\l \geq c_T)}
  \end{equation*}

  At the efficient level of capacity, the expected price given that
  the price is above variable cost is equal to that variable cost plus the fixed cost of capacity
  discounted by the probability the price is above the variable cost.


  The expression on the right-hand side is often known as the \alert{long-run marginal cost (LRMC)}
  of a generator of type $T$. The LRMC is equal to the variable cost plus the fixed cost (per unit of
  capacity) discounted by the probability that the generator is operating.

\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
  \includegraphics[width=8.5cm]{multiple-price-duration}

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




\begin{frame}{Multiple generators with inelastic demand}

  Assume again we have $c_1 \leq c_2 \leq \cdots \leq c_N$ and $S_n = \sum_{i=1}^n K_i$
  then:
  \begin{equation*}
    \l_t = \left\{ \begin{array}{ll}
      V& \textrm{ for } Q_t > S_N \\
      c_i & \textrm{ if } S_{i-1} < Q_t \leq S_i, \hspace{1cm} \textrm{ for } i = 1, \dots N
    \end{array}\right.
  \end{equation*}

  Looking at the area under the price duration curve but above the
  variable cost, we then find:
  \begin{equation*}
    f_i = (V-c_i)P(Q>S_N) + \sum_{j=i+1}^N (c_j-c_i) P(S_{j-1} < Q \leq S_j)
  \end{equation*}


\end{frame}


\begin{frame}{Screening curve}

  These equations can be rewritten recursively using the substitution
  $\theta_i = P(Q>S_i)$ (see Exercise Sheet 4):
  \begin{align*}
    f_N + \theta_N c_N &= V\theta_N \\
    f_i + \theta_i c_i &= f_{i+1} + \theta_i c_{i+1} \hspace{1cm} \forall i = 1, \dots N-1
  \end{align*}
  The first equation can be solved to find $\theta_N$, then the other equations can be solved recursively to find the remaining $\theta_i$. The $\theta_i$ correspond to the optimal \alert{capacity factors} of each type of generator, which correspond to the fraction  of time the generator runs at full power.


\end{frame}

\begin{frame}{Screening curve}

  The costs as a function of the capacity factors can be drawn
  together as a \alert{screening curve} (more expensive options are
  \emph{screened} from the optimal inner polygon).

  The intersection points determine the optimal capacity factors and hence, using the load duration curve, the optimal capacities of each generator type.

  \centering
  \includegraphics[width=10.5cm]{screening-curve}

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



\begin{frame}{Screening curve versus Load duration}


  \centering
  \includegraphics[width=6.5cm]{screening-load-duration}

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

\section{Market-Based Investment in Electricity Generation}

\begin{frame}{Relation to individual investment decisions}

  Consider a generator who is a price taker for the price $\l_t$ at
  each time and who can invest even in small amounts of capacity. The expected value of his profit $\pi$ is then
  \begin{align*}
    \mathbb{E}(\pi)  = \sum_{t: \l_t \geq c} p_t (\l_t - c) - f
  \end{align*}

  The generation entrepreneur will add a small amount of capacity of
  this generation type if and only if this expression is
  positive. Similarly, the generation entrepreneur will withdraw a
  small amount of capacity of this generation type if this expression
  is negative. Therefore, we can conclude that in a
  free-entry-and-exit equilibrium, this expression will be zero.
\end{frame}



\begin{frame}{Relation to individual investment decisions}

  Turning this around we get the same expression for $f$ as before:
  \begin{align*}
   f = \sum_{t: \l_t \geq c} p_t (\l_t - c)
  \end{align*}

  So: Under the assumptions we just set out, in a free-entry-and-exit
  equilibrium, with a high level of competition between generators,
  the equilibrium level of capacity chosen for each type of generator
  is optimal.

  But how does this work in practice?
\end{frame}



\begin{frame}{Grit in the machine 1/2}

  Several factors make this theoretical picture quite different in reality:
  \begin{itemize}
  \item Generation investment is \alert{lumpy} i.e. you can often only
    build power stations in e.g. 500~MW blocks, not in continuous chunks.
  \item Some older generators have \alert{sunk costs}, i.e. costs which have been incurred once and cannot be recovered, which alters their behaviour (i.e. the $f$ term is not evenly distributed across all hours)
  \item Returns on scale in building plant are not taken into account (we did everything linear)
  \item Site-specific concerns ignored (e.g. lignite might need to be near a mine and have limited capacity)
  \item Variability of production for wind/solar ignored
    \item There is considerable  uncertainty given load/weather conditions during a year, which makes investment risky; economic downturns reduce electricity demand
  \end{itemize}

\end{frame}


\begin{frame}{Grit in the machine}

  Several factors make this theoretical picture quite different in reality:
  \begin{itemize}
    \item Fuel cost fluctuations, building delays which cost money
  \item Risks from third-parties:  Changing costs of other generators, political risks (\co2 taxes,  Atomausstieg, subsidies for renewables, price caps)
  \item Political or administrative constraints on wholesale energy
    prices may prevent prices from rising high enough for long enough
    to justify generation investment (``Missing Money Problem'')
  \item  Lead-in time for planning and building, behaviour of others, boom-and-bust investment cycles resulting from periods of under- and over-investment in capacity
    \item Exercise of \alert{market power}
  \end{itemize}

\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}{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 Australian market, a MPC of A\$13,800/MWh for the 2015-2016 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.

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

  \centering
  \includegraphics[width=5.5cm]{price-cap}

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


\begin{frame}{Australian Market in Future}

  A recent paper on the Australian market:  ``100\% Renewables in Australia: Will a Capacity Market be
  Required?'' by Jenny Riesz, Iain MacGill, 2013,
  \href{http://ceem.unsw.edu.au/sites/default/files/documents/SIW13_Riesz-CapacityMarkets-2013-09-02a.pdf}{link},
  analysed the effect high shares of renewables would have on the market and the MPC.

  ``However, most
  renewables have very low SRMCs, which in a competitive
  market is likely to lead to an increasing proportion of low
  priced periods. This has led to suggestions that a capacity
  market may be required in the Australian National Electricity
  Market (NEM). This analysis suggests that existing energy-
  only market mechanisms in the NEM have the potential to
  operate effectively in a 100\% renewables scenario, but success
  will rely upon two critical factors: (1) further increase to the
  already high Market Price Cap (MPC) of A\$12,900/MWh.
  Initial analysis suggests this may need to increase by a factor
  of six to eight.''

  (Australia is also interesting for having a market with 5 min
  dispatch intervals, compared to hourly for Day Ahead in Germany and
  quarter-hourly for Intraday Market)

\end{frame}


\begin{frame}{Australian Market in Future}

  MPC may have to increase 6-8 fold to close to VOLL with high shares
  of RE so that conventional backup generators can recover their
  costs:

  \centering
  \includegraphics[width=8cm]{jenny_riesz}

  \source{Jenny Riesz}

\end{frame}




\begin{frame}{UK price spikes}

  Price spikes are also caused by reliability problems with other
  generators, as has happened recently in the UK:

  \centering
  \includegraphics[width=8cm]{uk_price_spike}
  \source{Financial Times}
\end{frame}

\begin{frame}{Comparison with Uber surge pricing}
  Note the same, since no long-term investments that need to be covered.

  Similar in terms of political concerns.

\end{frame}


\begin{frame}{Capacity Markets}
  A cap on the price in the wholesale market that is binding at times
  reduces the revenue that generators can earn from the market thereby
  reducing their incentives to invest. This is known as the ‘missing
  money’ problem and results in an inefficient mix of generation. The
  incentives for investment can be restored by making additional
  payments to generators based on their available capacity. These
  payments are often determined through a market process known as a
  ‘capacity market’. Capacity markets represent a response to an
  existing market defect (the price cap) and are not necessary where
  the price cap has been removed.

\end{frame}



\begin{frame}{Flexibilise demand}

  High price spikes can also be ameliorated by adjust demand, which
  was here assumed to be fairly inelastic.

  Flexibilise demand by making it price-responsive.

  The technology required to make a sufficient portion of the demand
  responsive to short-term price signals is not yet available,
  although some large loads (cement works, etc.) may already implement
  \alert{demand-side management (DSM)}.

  Widespread load disconnections are extremely unpopular and often
  have disastrous social consequences (accidents, vandalism). They are
  also economically very inefficient. Their impact can be estimated
  using the value of lost load (VOLL), which is several orders of
  magnitude larger than the cost of the energy not
  supplied. Consumers are not used to such disruptions and it is
  unlikely that their political representatives would tolerate them
  for any length of time.
\end{frame}


\section{Integrating Renewables in Power Markets}


\begin{frame}{Why do renewables need support at all?}

  NB: In some markets, they do not.

  \begin{itemize}
  \item Variability (unpredictable revenue leads to investor risk)
  \item Technology immaturity; needs support in early stage of learning curve
  \item External benefits not seen by market: lower pollution, \co2 emissions
  \item High ratio of capital costs to marginal costs require measures to reduce investment risk
  \end{itemize}
\end{frame}

\begin{frame}{Types of support schemes for renewables}

  \begin{itemize}
  \item No support at all (in some markets with good wind speeds,
    wind can survive on the spot market without any subsidy at all)
    \item Feed-In Tarriff (FIT, e.g. EEG - fixed payment per kWh for lifetime of project, often technology-specific,
      can also be region-specific, most popular form of RE subsidy worldwide)
    \item Contract for Difference (variation on the FIT, where market
      price is topped up to a set strike price)
    \item Production Tax Credit (essentially a tax discount corresponding to a direct subsidy per kWh)
    \item Quotas (E.g. Renewable Obligation Certificates in UK)
    \item Carbon taxes (increase relative cost of fossil fuels, but doesn't remove investor uncertainty)
  \end{itemize}



\end{frame}



\begin{frame}{Levelised Cost of Electricity (LCOE)}

  LCOE are full lifecycle costs per MWh including all fixed and
  variable costs.


  However it is FLAWED, doesn't take into account grid, balancing costs from uncertainty and backup costs.

\end{frame}


\begin{frame}{RE costs}

  \centering
  \includegraphics[width=10.5cm]{irena_costs}

  \source{\href{http://www.irena.org/DocumentDownloads/Publications/IRENA_RE_Power_Costs_2014_report.pdf}{IRENA Renewable Generation Costs}}
\end{frame}



\begin{frame}{Residual load curve}

  Simplest: subtract from load.

  \centering
  \includegraphics[width=10.5cm]{residual-load}

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


\begin{frame}{Residual load curve and screening curve}


  \centering
  \includegraphics[width=5.5cm]{residual-screening_curve}

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




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}{Copyright}


  Unless otherwise stated the graphics and text is Copyright
  \copyright Tom Brown and Mirko Sch\"{a}fer, 2016.

  We hope the graphics borrowed from others have been attributed
  correctly; if not, drop a line to the authors and we will correct
  this.

  The source \LaTeX, self-made graphics and Python code used to
  generate the self-made graphics are available on the course website:

  \url{http://fias.uni-frankfurt.de/~brown/courses/electricity_markets/}

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

  \begin{center}\ccbysa\end{center}

\end{frame}

\end{document}
