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# Risk aversion in flexible electricity markets

Thomas Möbius1, Iegor Riepin1, Felix Müsgens1, Adriaan H. van der Weijde2,3 1
Brandenburg University of Technology Cottbus-Senftenberg, Siemens-Halkse-Ring
13, 03046 Cottbus, Germany; 2 The University of Edinburgh, School of
Engineering, Robert Stevenson Road, The King’s Buildings, Edinburgh EH9 3FB,
UK; 3 The Alan Turing Institute, 96 Euston Rd, London NW1 2DB, UK.
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
(Date: August 27, 2024)

###### Abstract.

Flexibility options, such as demand response, energy storage and
interconnection, have the potential to reduce variation in electricity prices
between different future scenarios, therefore reducing investment risk.
Moreover, investment in flexibility options can lower the need for generation
capacity. However, there are complex interactions between different
flexibility options. In this paper, we investigate the interactions between
flexibility and investment risk in electricity markets. We employ a large-
scale stochastic transmission and generation expansion model of the European
electricity system. Using this model, we first investigate the effect of risk
aversion on the investment decisions. We find that the interplay of parameters
leads to (i) more investment in a less emission-intensive energy system if
planners are risk averse (hedging against CO2 price uncertainty) and (ii)
constant total installed capacity, regardless of the level of risk aversion
(planners do not hedge against demand and RES deployment uncertainties).
Second, we investigate the individual effects of three flexibility elements on
optimal investment levels under different levels of risk aversion: demand
response, investment in additional interconnection capacity and investment in
additional energy storage. We find that that flexible technologies have a
higher value for risk-averse decision-makers, although the effects are
nonlinear. Finally, we investigate the interactions between the flexibility
elements. We find that risk-averse decision-makers show a strong preference
for transmission grid expansion once flexibility is available at low cost
levels.

Keywords: Risk aversion, Energy storage, Interconnection, Demand response,
Investment.

JEL Classification codes: C6, Q4

##  1\. Introduction

Investments in electricity transmission and generation capacity are made under
a significant amount of uncertainty. The sources of this uncertainty include,
among others, the future levels and spatio-temporal distributions of
electricity demand, fuel costs and future energy policy. In recent years,
these uncertainties have arguably increased due to the ongoing evolution of
supply- and demand-side technologies and rapid policy changes designed to
encourage a transition to low-carbon energy systems. Because transmission and
generation investments have long lead times and are difficult to reverse, they
are subject to a large – and arguably increasing – amount of risk.

As in most markets, investors in electricity markets are usually risk averse
([34, 30, 26]. This risk aversion arises from the risk aversion of individual
decision-making agents within firms, the use of risk mark-ups on the expected
return on investment, the use of risk-averse probabilistic metrics by the
institutions that finance new projects, and other factors. There is evidence
that, separately from the increase in energy investment risk, investor risk
aversion itself is increasing as a result of the participation of less
traditional actors, such as institutional investors, in energy markets ([30]).
Therefore, the literature on transmission and generation planning has begun to
include risk-averse objectives in planning models (e.g. [15, 10, 7, 24, 1].
Although the exact impacts of risk aversion differ according to the specifics
of the settings analysed and the types of uncertainty considered, most of
these studies show that risk aversion significantly changes optimal
transmission and generation expansion plans.

These insights are useful. However, the existing literature has several gaps
that we aim to address in this paper. Most importantly, previous studies have
tended to analyse current electricity markets, which feature only limited
deployment of flexibility elements, such as energy storage, demand response
and international integration. In all likelihood, future electricity markets
will significantly increase the deployment of these flexibility elements. This
is especially important in the context of risk aversion. These sources of
flexibility will enable the more efficient integration of low-carbon
generation technologies, allowing fuel price and carbon price risk to be
addressed at lower cost. They can also reduce demand-side risk by decreasing
demand peaks. Finally, flexible technologies can reduce spatial risks by
allowing electricity to be transported more efficiently. Therefore, the risk
profiles of future electricity markets are likely to differ substantially from
those of current markets; by extension, the effects of risk aversion will
change as well.

A second, closely related gap is that the existing literature not only tends
to analyse relatively inflexible electricity markets, it also generally does
not explicitly include investment in flexible technologies such as storage or
interconnection. In addition to their different risk profiles, flexible
systems offer a wider set of investments that can be undertaken to mitigate
risk exposure. These may include investment decisions in flexible technologies
in addition to generation capacity.

Third, the existing literature on risk aversion includes renewable investment
as an endogenous variable. Since renewable investment is an effective hedge
against fuel and carbon price risk, as has been shown in the literature (e.g.
[24]), it often drives model results; suggesting a higher amount of investment
in renewables when decision-makers are risk averse. In many jurisdictions,
however, renewable investment is driven more by policy and central planning
than by market forces. Therefore, such investment might not serve as a
relatively inexpensive hedge against high fuel or carbon prices.

In this paper, we explicitly analyse the interactions between risk aversion
and flexibility. Since international interconnection is one of the most widely
recognised elements of flexibility, we cannot simply focus on a single
electricity market but instead consider a series of linked markets. This
simultaneously addresses a fourth gap in the existing literature on risk
aversion, which typically focuses on individual markets even though investors
often operate across markets. Our case study focuses on the European
electricity market, which consists of several linked but independent national
markets. Using an integrated planning model applied to a simplified
representation of the European electricity grid, we consider three types of
flexible technologies: increasing interconnection between national markets,
energy storage investment and demand flexibility. As mentioned above,
increasing interconnection provides flexibility because it allows the movement
of electricity – especially low-cost renewable electricity – in space. Energy
storage can move electricity in time. Finally, demand flexibility allows
consumers to more efficiently signal their valuation of electricity, allowing
scarce resources to be allocated more efficiently and reducing the need for
investment in peak-load capacity with low utilisation rates.

We analyse the impact of each of these sources of flexibility on the system in
turn and then also consider the interactions between them. Of particular
importance are the interactions between increasing interconnection and demand
flexibility. Since each country has its own distinct industry structure, with
different levels of willingness to pay between industries and between
countries, increasing flexibility can increase overall efficiency but also
significantly affect the spatial distribution of investment and net demand.
Unlike earlier studies, we consider renewable investment to be exogenous (i.e.
determined by existing long-term national renewable expansion plans rather
than by electricity market prices) but stochastic (i.e. there is uncertainty
about how successful current plans will be). We also consider demand, fuel
price and carbon price uncertainty using an inter- and extrapolation of the
widely used ENTSOs Ten-Year Network Development Plan (TYNDP) scenarios ([12]).

This approach allows us to address the four gaps identified above. In addition
to contributing to the literature on risk-averse planning by generalising it
to flexible energy systems, we also advance the literature on the value of
flexibility elements by including the value of energy storage, interconnection
and demand response. We generalise this literature by including the value of
flexibility in terms of risk reduction, which, as we will see, is important if
decision-makers are risk averse.

In line with the previous literature, we find that risk aversion significantly
affects investments in transmission and generation capacity. Although we
include uncertainty in demand, renewable capacity and fuel prices, we find
that carbon price uncertainty generates the highest level of investment risk
in the European context. In response, risk aversion decreases investment
incentives especially for high-emission technologies despite the risk of
failing to meet electricity demand. Conversely, risk aversion increases
investment in international interconnection capacity when this option is
available. Risk aversion also increases incentives to invest in energy storage
and to utilise demand flexibility. Finally, there are important nonlinear
interactions between these flexibility elements. In particular, when all
flexibility options are available at low cost, risk-averse system planners
increasingly use the interconnection expansion option, reducing the reliance
on demand flexibility and storage expansion. When flexibility options are
available but more expensive, the opposite happens.

The next section briefly reviews the existing literature on risk aversion in
electricity markets. Section 3 sets out the details of our modelling
methodology. Section 4 provides all our assumptions regarding the scenarios
and data. Our results are presented in Section 5 and discussed in Section 6.
Section 7 concludes.

##  2\. Literature review

Questions concerning optimal or expected generation and transmission capacity
expansions have been a subject of research for decades. A wide range of models
have been developed to help determine optimal transmission expansion plans,
simulate prices and investment incentives under different future scenarios,
determine the impact of market design changes, among others. Early models were
deterministic and often tailored towards either generation or transmission
expansion in isolation. Currently, the most common approach integrates
transmission and generation expansion into a multi-level partial equilibrium
model of the electricity sector. If markets are assumed to be perfectly
competitive, which is the usual approach, and transmission planners are
assumed to maximise social surplus, the problem can be condensed into a
single-level optimisation model ([17]).

One key finding that has been shown repeatedly is that explicitly considering
uncertainty is important when modelling generation and transmission expansion.
Models that rely on the heuristic application of deterministic models lead to
a significant cost of ignoring uncertainty, as shown by [28], who investigate
the expected costs of ignoring uncertainty for investments in an integrated
electricity and gas market model. In response to this, and to rapid decreases
in the computational cost of large-scale models, stochastic capacity expansion
models have become more common (e.g. [33, 27, 1]).

Most stochastic studies use simple expected-value optimisation models. While
such models are useful, they do not account for the fact that real-world
investors are risk averse and therefore under- or overestimate investment
incentives for particular technologies or locations. In response, risk-averse
objectives have been included using either nonlinear utility functions (e.g.
[15]) or, more recently, coherent risk metrics (e.g. [24]). These studies show
that, like uncertainty, risk aversion changes investment strategies.
Generally, higher levels of risk aversion lead to more investment in
renewables ([32, 20, 9]) complemented by lower-cost thermal capacity ([10]),
although the precise implications depend heavily on the types and relative
magnitudes of the uncertainties considered.

At the same time, scholars have shown increasing interest in considering
investment options other than straightforward transmission and generation
capacity. Studies have examined storage investment (e.g. [16, 3]), investment
in the presence of demand response ([8]) investment in power plant flexibility
([18]), market-participating residential microgeneration ([4]), as well as
other demand-side flexibility options ([22]).

So far, however, little attention has been paid to the interactions between
risk aversion and flexibility in electricity markets. These interactions are
clearly important. [9] use a risk-averse stochastic planning model to show
that electricity storage reduces price risk and is therefore more attractive
as part of a risk-averse portfolio. The same is likely to be true for other
flexibility options. There are also obvious interactions between different
types of flexibility. For instance, [6] use a simple statistical model to
demonstrate that interconnection and load shedding, which can be thought of as
a last-resort type of demand flexibility, are substitutes. [6] also show that
in connected asymmetric markets, the effects of adding flexibility options
will also be asymmetric, with some markets benefiting more than others.

Therefore, there is a gap in the existing literature, which we aim to address
in this paper. We consider the interactions between risk aversion and three
types of flexibility: demand response, international interconnection and
energy storage. As we are interested in empirical results in addition to
theoretical effects, we employ a large stochastic model of the European
electricity system combined with a widely used set of scenarios and a detailed
representation of demand flexibility. Instead of the common approach, which
uses continuous direct demand functions which are often difficult to
parameterise, we approximate the real-world flexibility of demand by
constructing piecewise linear demand functions based on the different
components of electricity demand in each market and their estimated value of
lack of adequacy (VoLA111[5] defines this as the equivalent of the value of
lost load (VoLL) when notice is provided one day ahead of the supply
interruption). We exogenously vary the amount of these flexible options to
determine their individual and joint effects, but also consider cases where
investment in storage and interconnection is endogenous.

##  3\. Methods

In this section, we first present a general form of the stochastic
optimisation problem that we apply. Second, we introduce our approach to
modelling the risk aversion of market participants. Third, we explain how we
translate this approach to a large-scale optimisation model of the European
electricity market. Fourth, we discuss the input data for the model.

###  3.1. Two-stage stochastic optimisation

Consider a linear optimisation problem (LP) where $x$ represents a vector of
variables, $c$ and $b$ are vectors of parameters, $A$ is a matrix of
parameters and $T$ is a matrix transpose. The inequalities specify a convex
polytope that constrains the objective function. The optimal deterministic
solution (DS) is to find a vector $x$ that minimises the objective function
given a set of constraints:

$\begin{array}[]{l}DS:=\displaystyle\min_{x}c^{T}x\\\ \textrm{s.t. }Ax\geq
b,x\geq 0\end{array}$ (1)

Deterministic linear problems of this type can be scaled to large optimisation
problems with high levels of empirically relevant detail for the energy
sector. They can then be solved with efficient linear solvers such as CPLEX
and Gurobi.

However, whenever energy planners attempt to construct a model of a real-world
electricity market, they are faced with multiple parametric uncertainties.
This is true irrespective of the application domain. These uncertainties
include (market-driven) prices for energy carriers, the future development of
demand levels and CO2 prices, structural changes in the energy sector (e.g.
nuclear phase-outs), regulation (e.g. decolonisation policies and the
subsidisation of renewable generation) and many more factors.

In the literature, this parametric uncertainty is typically addressed
_reactively_ – through sensitivity analyses – or _proactively_ – through
stochastic programming formulations ([23]). The aim of the first approach is
to reveal the impact of data perturbations on a model’s recommendations. Such
an exercise is _reactive_ in that it only discovers the impact of data
uncertainty on model outputs and requires a predefined heuristic rule to make
a decision that is _good enough_ given all the scenarios under consideration.

The aim of the (_proactive_) approach is to explicitly incorporate uncertainty
as part of the optimisation problem. This can be done by formulating a two-
stage stochastic linear optimization problem that uses a probability
distribution or scenario set to describe the uncertain parameters. In such a
problem, the optimal _first-stage_ decisions must be made before the
information about uncertain parameters is revealed, while the _second-stage_
decisions are made after it is revealed. The general form of a two-stage
stochastic LP as described in [2] is as follows:

$\begin{array}[]{l}SS:=\displaystyle\min_{x}c^{T}x+\mathbb{E}_{s}[Q(x,s)]\\\
\textrm{s.t. }Ax\geq b,x\geq 0\\\ \end{array}$ (2)

$\begin{array}[]{l}\textrm{where}\\\
Q(x,s):=\displaystyle\min_{y}q^{T}_{s}y\\\ \textrm{s.t. }T_{s}x+W_{s}y\geq
d_{s},y\geq 0\\\ \end{array}$ (3)

where $x$ denotes the vector of first-stage variables, $y$ is the vector of
second-stage variables and $s$ is the vector of uncertain data (i.e. the
discrete set of scenarios that include a finite number of scenarios with
differences regarding the uncertain parameters). Each scenario $s\in S$ occurs
with a probability $\sum_{s}\pi_{s}=1$. The first-stage parameters
($c^{T},A,b$) in Eq. (2) are assumed to be known with certainty. The second-
stage decisions in Eq. (3) are restricted by the first-stage decisions $x$,
and the parameters ($q,T,W,d$) are actual realisations of uncertain data (i.e.
the solution must be feasible for every scenario $s\in S$). Overall, the
first-stage problem seeks to minimise the sum of the costs of the first-stage
decisions and the _expected_ costs of the second-stage decisions. The second-
stage problem accordingly seeks to minimise the second-stage costs.

In the context of our electricity market application, solving problem (2–3)
implies finding both (i) the optimal _first-stage_ investment decisions for
power generation and transmission capacities $\hat{x}$ under uncertainty by
considering the probability of the uncertain events222Note that investment
decisions must hold for _all realisations_ of $s\in S$ and (ii) the optimal
_second-stage_ dispatch decisions (generation, storage and demand response)
for _each realisation_ of $s\in S$ (i.e. after market agents have full
knowledge of the uncertain parameters).

###  3.2. Modelling risk aversion

As discussed above, individual decision-making agents in the electricity
markets are usually risk averse. Hence, we include risk aversion in the
objectives of the mathematical models when modelling investment decisions and
system development. In general, this involves replacing the expectation
operator in 2 with a risk measure. In line with the previous literature (e.g.
[24]), we use a convex combination of the second-stage expected value and the
conditional value at risk (CVaR) ([29]). The CVaR is a coherent risk measure
that effectively increases the weight on the $1-\alpha\%$ worst outcomes,
where ‘worst’ is defined endogenously. Since it is the solution to a linear
optimisation problem, it can easily be integrated into the stochastic
framework described above. Increasing the weight of a discrete set of worst
outcomes is also consistent with the use of P90 percentiles and threshold
values in energy finance ([21]), which is one reason why investors are often
risk averse.

###  3.3. The stochastic optimization problem for European electricity markets
with risk aversion

Following the model structure outlined above, we develop and apply a
stochastic large-scale optimisation model of the European electricity sector
considering risk-averse decision-makers. The model results include spatial and
temporal decisions about investments in electricity generation, transmission
and storage capacities, as well as decisions about the generation, trade and
storage of electricity.

The geographic scope of the model includes most EU27 member states333Cyprus,
Ireland, Iceland and Malta are not included, Norway, Switzerland and the
United Kingdom. The single market zones are connected through net transfer
capacities (NTCs). A list of the regions considered is presented in Appendix
B. The temporal scope of the model includes three representative years: 2020,
2025 and 2030; each year is modelled by 350 representative operational hours.
This approach ensures the inclusion of both long-term investment dynamics and
the short-term dispatch of infrastructure elements. Investment decisions are
made once, at the beginning of the modelled period.

In the following, we present our optimisation model. We first establish a
nomenclature and then provide all relevant model formulations.

####  3.3.1. Nomenclature

Note that we use capital letters for all sets and parameters except for the
parameters $\alpha$, $\eta_{i}$, $\rho_{s}$ and $\omega$.

####  3.3.2. Model formulation

The objective function in Eq. 4 minimises total system costs considering the
costs of all first-stage investments $IC$ and second-stage operation costs
$OC$. With increasing risk aversion, decision-makers give a higher weight
$\omega$ to the riskiest scenarios considered in $cvar$.

$\displaystyle\min
TC=IC+(1-\omega)\sum_{s}\rho_{s}\mathit{OC}_{s}+\omega\mathit{cvar}$ (4)

The investment costs $IC$ include all discounted annualised investments in
power generation capacities $x_{i,n,y}$, cross-border transmission capacities
$y_{n,nn,y}$ and pumped-storage plant (PSP) capacities $z_{psp,n,y}$.

$\displaystyle
IC=\sum_{y}DF_{y}\left(\sum_{i,n}CX_{i,y}x_{i,n,y}+\sum_{n}CY_{n,nn,y}y_{n,nn,y}+\sum_{n}CZ_{y}z_{psp,n,y}\right)$
(5)

Note that the investments made are irreversible. Therefore, the annuities for
the investments made at the beginning of the model period must be taken into
account in all subsequent years.

$\displaystyle
x_{i,n,y}-x_{i,n,y+1},y_{n,nn,y}-y_{n,nn,y+1},z_{psp,n,y}-z_{n,y+1}\leq 0$ (6)
$\displaystyle\forall i\in I,n,nn\in N,y\in Y$

Eqs. 7 and 8 take into account the country-specific technical and political
restrictions that limit investments in power generation and storage capacity.
For example, countries with a nuclear phase-out strategy cannot invest in
nuclear power plants.

$\begin{array}[]{l l}x_{i,n,y}\leq X^{max}_{i,n}&\forall i\in I,n\in N,y\in
Y\\\ \end{array}$ (7)

$\begin{array}[]{l l}z_{psp,n,y}\leq Z^{max}_{n}&\forall n\in N,y\in Y\\\
\end{array}$ (8)

In the second stage, the operational decisions are made depending on the
scenario realisation $s$. Therefore, the second-stage operational costs $OC$
include discounted costs of electricity production and demand response.

$\displaystyle
OC_{s}=\sum_{y}DF_{y}\left(\sum_{i,n,t}VC_{i,n,y,s}g_{i,n,t,y,s}+\sum_{sec,n,t}VOLA_{sec,n,y}shed_{sec,n,t,y,s}\right)$
(9) $\displaystyle\forall s\in S$

To define the CVaR, we apply the approach used in [24].

$\displaystyle\zeta+\frac{1}{1-\alpha}\sum_{s\epsilon S}\rho_{s}a_{s}\leq
cvar$ (10)

$\begin{array}[]{l l}\displaystyle a_{s}\geq OC_{s}-\zeta&\forall s\in S\\\
\end{array}$ (11)

Eq. 12 ensures efficient market clearing, where demand $D_{n,t,y,s}$ always
equals the sum of generation $g_{i,n,t,y,s}$ of all conventional, renewable
and storage technologies, increased by imports $flow_{nn,n,t,y,s}$ and reduced
by exports $flow_{n,nn,t,y,s}$ and the energy withdrawal of storage facilities
$pump_{psp,n,t,y,s}$.

$\displaystyle
D_{n,t,y,s}=\sum_{i}g_{i,n,t,y,s}-\sum_{psp}pump_{psp,n,t,y,s}+\sum_{nn}(flow_{nn,n,t,y,s}$
(12) $\displaystyle-flow_{n,nn,t,y,s})+\sum_{sec}shed_{sec,n,t,y,s}\hskip
10.00002pt\forall n\in N,t\in T,y\in Y,s\in S$

Electricity generation is constrained by the existing capacities
$\mathit{CAP}_{i,n,y}$, new investment $x_{i,n,y}$ and availability factors
$AF_{i,n,t,y}$. Note that neither intermittent nor dispatchable renewables are
subject to investment decisions since the expansion path for these
technologies is implemented exogenously and is subject to uncertainty.
Curtailment occurs in cases where renewable generation is lower than available
capacity. Penalty payments for renewable curtailment are not considered.

$\begin{array}[]{l l}\displaystyle
g_{i,n,t,y,s}\leq(CAP_{i,n,y}+x_{i,n,y})AF_{i,n,t,y}&\forall i\in I,n\in
N,t\in T,y\in Y,s\in S\\\ \end{array}$ (13)

We model demand response through a supply function derived from sector-
specific values of lost adequacy (VoLAs), as explained in more detail below.
Therefore, hourly sector-specific demand reductions in each sector are limited
to the sectoral electricity consumption in the respective hour.

$\displaystyle shed_{sec,n,t,y,s}\leq D_{n,t,y,s}SHARE_{sec,n}$ (14)
$\displaystyle\forall sec\in SEC,n\in N,t\in T,y\in Y,s\in S$

Our model also considers energy storage. For this purpose, we exclusively
consider PSPs. The hourly pumping capacity of PSPs $pump_{psp,n,t,y,s}$ is
restricted by their existing and newly built capacity. Note that turbine
generation is already addressed in Eq. 13.

$\displaystyle
pump_{psp,n,t,y,s}\leq(CAP_{psp,n,y}+z_{psp,n,y})AF_{psp,n,t,y}$ (15)
$\displaystyle\forall psp\in I,n\in N,t\in T,y\in Y,s\in S$

The storage level $sl_{psp,n,t,y,s}$ defines the water level in the upper
basin of a PSP. It increases due to pumping activities and decreases due to
the PSP’s electricity generation. Efficiency losses $\eta_{psp}$ are also
considered.

$\displaystyle
sl_{psp,n,t,y,s}=sl_{psp,n,t-1,y,s}+pump_{psp,n,t,y,s}\eta_{psp}-g_{psp,n,t,y,s}$
(16) $\displaystyle\forall psp\in I,n\in N,t\in T,y\in Y,s\in S$

The storage level is restricted to the maximum capacity of the upper basin of
a PSP, which is linked to the installed generation capacity and a
capacity–power factor. The capacity–power factor can be understood as the
number of full load hours a PSP can run until it is fully discharged.

$\displaystyle sl_{psp,n,t,y,s}\leq(CAP_{psp,n,y}+z_{psp,n,y})CPF$ (17)
$\displaystyle\forall psp\in I,n\in N,t\in T,y\in Y,s\in S$

Eq. 18 introduces a monthly water budget for hydro reservoirs that cannot be
exceeded due to the electricity generation of these power stations.

$\displaystyle\sum_{t\epsilon m}g_{hr,n,t,y,s}\leq
CAP_{hr,n,y}budget_{hr,n,m}$ (18) $\displaystyle\forall hr\in I,n\in N,m\in
M,y\in Y,s\in S$

The cross-border flow of electricity is constrained by the existing NTCs
$NTC_{n,nn,y}$ and newly built transfer capacities $y_{n,nn,y}$.

$\displaystyle flow_{n,nn,t,y,s}\leq NTC_{n,nn,y}+y_{n,nn,y}$ (19)
$\displaystyle\forall n\in N,nn\in N,t\in T,y\in Y,s\in S$

Non-negativity:

$\displaystyle
a_{s},g_{i,n,t,y,s},flow_{n,nn,t,y,s},pump_{psp,n,t,y,s},shed_{sec,n,t,y,s},sl_{i,n,t,y,s},x_{i,n,y},$
(20) $\displaystyle y_{n,nn,y},z_{psp,n,y},\geq 0\hskip 10.00002pt\forall i\in
I,sec\in SEC,n,nn\in N,t\in T,y\in Y,s\in S$

##  4\. Scenarios and Data

In this section, we explain the development of our scenarios and provide the
assumptions for the data used in our model.

###  4.1. Scenarios

We parametrise our model primarily based on the widely used Ten-Year Network
Development Plan (TYNDP) report published by ENTO-E ([12]). For the year 2030,
the TYNDP presents three scenarios describing possible energy futures:
distributed generation (DG), sustainable transition (ST) and the European
Commission’s core policy scenario (EUCO).

In the context of these scenarios, we identify four key parameters in the
electricity sector that are subject to uncertainty: electricity demand,
installed intermittent renewable energy source (RES) capacities (such as
onshore wind, offshore wind and photovoltaics), fuel prices and CO2 prices. In
the following, we briefly describe the scenarios and highlight their
assumptions.

The DG scenario assumes the development of a decentralised energy system with
a strong focus on end-user technologies. As a result, electric vehicles and
hybrid heat pumps see their highest penetration in this scenario, and
photovoltaics and battery systems are widely used. Of the three scenarios, DG
assumes the highest levels of electricity consumption (both peak and
cumulative) and the highest deployment of solar power.

The ST scenario assumes very high CO2 prices intended to achieve a sustainable
reduction of CO2, resulting in the replacement of hard coal and lignite by
gas-fired power plants. The electrification of other sectors, such as heat and
transportation, develops rather slowly. In comparison to the other scenarios,
ST shows the highest price for CO2 certificates (89.9 €2020/t in 2030) and the
lowest electricity demand.

Finally, EUCO represents the 2016 EU Reference Scenario. The scenario
represents a pathway to achieve the 2030 climate and energy targets agreed
upon by the European Council in 2014. Compared to the other scenarios, EUCO
shows the highest prices for lignite and hard coal and the lowest prices for
natural gas and oil. Additionally, EUCO assumes the lowest price for CO2
certificates (28.8 €2020/t in 2030).

Since we use the CVaR to analyse the effect of risk aversion, we must consider
more than three scenarios to meaningfully differentiate a small percentage of
tail scenarios from the others. We address this requirement by generating a
range of scenarios that are linear inter- and extrapolations of the TYNDP
scenarios. We also compute the expected value (EV), which we calculate as the
average of the three TYNDP scenarios. This allows us to generate three
additional scenarios by interpolating between the EV and each TYNDP scenario.
As a result, we define 22 scenarios for 2030. We assume that these scenarios
have equal probabilities of realisation. Figure 1 (left) illustrates the
construction of these 22 scenarios. We inter- and extrapolate each pair of
scenarios by weighting them with factors of -10%, 33%, 50%, 67% and 110%, thus
obtaining five new scenarios. The interpolation between a TYNDP scenario and
the EV is conducted using the mean of the two scenarios.

As mentioned before, our model horizon contains three representative years:
2020, 2025 and 2030. The year 2020 is assumed to be subject to no uncertainty.
Hence, all scenario paths begin with the same assumptions. These are based on
the ‘best estimate’ scenario, which also is provided by the TYNDP and
represents an intermediate step to the scenarios introduced. The uncertainty
regarding the four key parameters thus only occurs from 2025 onwards. The
investment decisions are made in the first stage and must hold for all
scenario realisations in the second stage. The scenario paths with the highest
(endogenous) operational costs form the CVaR and drive the investments of
risk-averse decision-makers.

Figure 1. Scenario generation (left) and scenario paths (right) based on TYNDP
scenarios.

###  4.2. Data

As mentioned above, scenario-specific assumptions regarding the uncertain
input parameters of electricity demand, installed capacities of RES and the
prices of fuel and CO2 are defined by the TYNDP report from [12]. A detailed
overview of the scenario data is provided in Appendix A.

Fuel prices that are not scenario-specific (e.g. prices for nuclear power
plants) are based on [31]. Node-specific thermal and hydro generation
capacity, efficiency and decommission pathways are derived from [31], [19],
[13] and [25].

Investment costs for new electricity generation and storage capacities are
derived from [31], and investment costs for transfer capacities are based on
[19]. Since we identify optimal investment decisions using three
representative years, we compute annualised capital costs and allocate them to
the respective year using an interest rate of 6%. Lifetime assumptions
regarding electricity generation and storage technologies are provided by [31]
and can be found in the supplementary material (https://github.com/BTU-
EnerEcon/RiskAv). For transfer capacities, we assume a lifetime of 50 years.

In reality, minimum capacity requirements ensure that new power plants are
economically viable; our model, however, excludes these requirements. Instead,
the model allows investment in marginal amounts of generation capacity, which
are grouped into capacity clusters. However, we consider political and
technical constraints on investments in generation capacities (e.g. the
installation of nuclear, lignite or hard coal plants is only possible in
countries without phase-out plans). Given the long planning horizon for most
generation technologies, we assume that a capacity expansion in 2020 is
feasible only for open cycle gas turbines. Run-of-river stations,
hydroelectric reservoirs, biomass and waste-to-energy are not subject to an
endogenous investment decision and follow a pre-defined expansion plan derived
from [13].

As storage technology, we consider only hydroelectric PSPs. These are modelled
with their turbine and pumping capacity as well as their storage capacity. We
connect these components assuming a capacity-power factor of nine, which is
defined as the number of hours a fully charged storage system can produce at
full load. Generation by hydroelectric reservoirs is constrained by the
installed capacities and a monthly water budget. To determine the water
budget, we use empirical electricity generation data; both empirical
electricity generation data and installed capacities are taken from [11].

Electricity generation from intermittent renewable capacities is not
dispatchable and depends on meteorological conditions. We implement hourly
feed-in profiles derived from [11] for onshore wind, offshore wind and
photovoltaics. Despite the existence of different ‘wind-years’, we assume that
the hourly feed-in profiles do not vary within our model horizon. For the
years considered (including their scenario variations), we adjust only the
capacity levels.

We allow for endogenous cross-border trade within the model’s geographical
scope. Electric power transmission between nodes is restricted by NTCs. We
apply current NTC values for the year 2020 and implement the currently planned
expansions until 2030. Hence, the endogenous investments in transfer
capacities are always additional to the current expansion plan. Both current
installations and currently planned expansions are taken from [12]. We neglect
intranational limitations on electricity flows.

We model demand response with a location-specific supply function for demand
reduction. Demand response activities, which are driven by a scarcity of power
plant capacity, are assumed to be remunerated by the value of lack of adequacy
(VoLA), which is individually determined for each industry sector and each
European country by [5]. For each country, we identify the sector-specific
share of electricity consumption [14] and link it to the hourly demand,
constructing a stepwise supply function for load shedding activities. The
resulting values are made available in the supplementary material
(https://github.com/BTU-EnerEcon/RiskAv). When we apply these supply
functions, we implicitly assume that each sector can perfectly signal its
value of electricity to the market, such that if the costs of meeting
(sectoral) demand exceed the (sectoral) valuation of electricity, the market
outcomes include a reduction in demand. In what follows, we use the terms
demand reduction’ and ‘load shedding’ as synonyms since all load shedding in
our model is planned rather than a result of unexpected contingencies. Note
that while domestic electricity consumption is included as one of the sectors,
it is unlikely to be called upon since it has a much higher VoLA than most
others.

Since our optimisation model minimises the present value of the electricity
system’s total cost, all future costs are discounted. We apply a discount rate
of 6% per year.

##  5\. Results

This section is structured as follows. First, we illustrate the impact of risk
aversion on investments in our base case, with all flexibility options (demand
response, international trade and storage) at their current levels. Second, we
vary the availability and cost of individual flexibility options to examine
their impact on the risk mitigation measures taken by risk-averse planners.
Finally, we analyse the effects of the interplay between flexibility elements.

###  5.1. Base case

######  Result 1.

Risk-averse decision-makers consider the combined effect of all uncertainties.
Since uncertainties are correlated and have different levels of impact, this
can lead to counterintuitive effects. In our case, risk aversion has little
impact on overall generation investment despite the presence of demand
uncertainty. This effect occurs because uncertain CO2 prices have a larger
impact on investment decisions than other uncertainties, and CO2 prices
correlate negatively with demand levels in the framework of the TYNDP
scenarios.

Risk-averse investment planning aims to avoid the very worst outcomes. Hence,
investment decisions in a system with risk-averse agents differ from those
made under risk-neutral decision-making. Assuming a hypothetical naïve
approach in which a risk-averse planner addresses each uncertainty
individually, one can derive the following principles for the four key
uncertainties considered in our paper:

  1. (1)

Demand uncertainty would be addressed by installing more peak-load capacity,
reducing costly load shedding in times of demand spikes.

  2. (2)

Like demand uncertainty, uncertainty about RES capacities would be addressed
by installing more peak-load capacity, reducing the costly use of demand
flexibility in times of low RES feed-in.

  3. (3)

CO2 price uncertainty would be addressed by favouring investments in low-
carbon technologies.

  4. (4)

Fuel price uncertainty would be addressed by favouring investments in
technologies with lower price uncertainty.

Assuming that the naïve approach is applied to mitigate the combined risk of
the four uncertain parameters, a risk-averse planner could be expected to
reduce risk by installing more generation capacity consisting of more low-
carbon generators and generators with less variation in fuel costs.

Figure 2 presents the aggregated European capacity investments through 2030
for different levels of risk aversion, from risk neutrality in
$\omega\textsubscript{1}$ to very strong risk aversion in
$\omega\textsubscript{6}$. Notably, risk-averse planning produces results
within the framework of the TYNDP scenarios that deviate from the intuitions
derived above. As risk aversion increases, we observe no increase in secured
capacities, while aggregated European load shedding activities increase by
roughly 30% and the shedding costs increase by 70%. This highlights that risk-
averse system planners do not focus on installing more capacity.

Furthermore, the investment mix has a clear trend in $\omega$. Figure 2 shows
that, in a risk-neutral setting, significant investments are made in lignite-
fired generation capacity. With increasing risk aversion, lignite disappears
from the energy mix, while nuclear technology enters it. This highlights the
significant influence of CO2 price uncertainty on decisions made by risk-
averse planners. The risk of very high CO2 prices pushes risk-averse planners
to invest in more capital-intensive but emission-free nuclear power plants.
The trend depicted in Figure 2 shows that higher risk aversion corresponds to
more emission-free nuclear capacity. In addition, we observe no open cycle gas
turbine (OCGT) investment in $\omega\textsubscript{6}$. This can be explained
by the scenarios with high CO2 prices, which receive a very high weight if
decision-makers are extremely risk averse, and the relatively low efficiency
of the OCGT technology.

Figure 2. Aggregated European capacity investments until 2030 (left) and
aggregated European load shedding activities and load shedding costs in 2030
(right) in risk-aversion scenario

To further examine these results, we plot the parametric assumptions of each
of our 22 scenarios in Figure 3. Note that the demand and RES deployment
scenarios can be illustrated together by plotting maximum hourly residual
values. The scenarios that risk-averse planners consider as particularly risky
and/or difficult to mitigate (i.e. those that are endogenously included in the
CVaR tail and receive a higher weight) are highlighted.

As Figure 3 shows, the tail scenarios are exclusively the scenarios with the
highest CO2 prices. Because the TYNDP scenarios are internally consistent, the
highlighted scenarios also have the lowest maximum residual loads, which means
that they do not require extensive capacity investments to meet demand.
Moreover, in the tail scenarios, lignite and hard coal prices tend to be low,
while gas and oil prices tend to be high. Despite low lignite prices, risk-
averse planners prefer to invest in nuclear capacity to hedge against the risk
of high CO2 prices.

Thus, the interplay of parameters leads to (i) more investment in a less
emission-intensive energy system if planners are risk averse (hedging against
CO2 price uncertainty) and (ii) constant total installed capacity, regardless
of the level of risk aversion (planners do not hedge against demand and RES
deployment uncertainties).

Figure 3. Scenario-specific CO2 price (left), maximum hourly residual load
aggregated for Europe (centre) and fuel prices (right) for the year 2030. The
dots marked with red circles depict the scenarios that the risk-averse planner
considers particularly risky.

###  5.2. Risk aversion and flexibility elements

Usually, more flexibility in electricity markets reduces investment risk,
since flexibility options both reduce short-term price variability within
scenarios and allow the electricity system to more efficiently adapt to long-
term uncertainty between scenarios. Therefore, we would expect the
availability of flexibility options to reduce the cost of risk mitigation in
risk-averse system planning, thus reducing the effects of risk aversion. In
this section, we investigate the impact of flexibility elements on a system in
which decision-makers are endowed with different levels of risk aversion. We
focus our discussion on three key flexibility elements of electricity markets:
demand response, cross-border trade and energy storage.

Each flexibility element has its own mechanism and dynamics. Demand response
allows consumers to react to price spikes by reducing demand, receiving the
sector-specific load shedding supply cost (VoLA444The value of lack of
adequacy (VoLA) is described in section 4.2) in return. Cross-border trade
enables spatial transfers of electricity between regions with price
differences and is limited by the availability of NTCs. Energy storage enables
temporal transfers between periods with different prices.

In sections 5.2.1–5.2.3, we examine the effects of the individual flexibility
elements in isolation. Finally, in section 5.2.4 we analyse the interplay of
the three flexibility elements.

In our discussion, we refer to the ex-post expectation of total system costs,
which is the sum of all first-stage investment costs for generation, storage
and cross-border transmission capacity expansion, plus a risk-neutral
expectation of the second-stage operating costs. We use this metric instead of
the ex-ante risk-averse expectation of total costs because the latter, by
definition, increases with risk aversion since higher weights are placed on
the costliest scenarios. Therefore, it would be difficult to disentangle the
effects on total costs of a change in first-stage decisions from the effects
of a simple change in scenario weights. Using a risk-neutral ex-post
expectation isolates the effect on costs of a change in investment.
Nevertheless, it is important to keep in mind that this metric is a
mathematical construct and not the model objective. This means that, unlike
the model objective, it can decrease even if we give the model more
flexibility options to invest in.

####  5.2.1. The isolated effect of demand response

######  Result 2.

The value of demand flexibility generally increases with higher levels of risk
aversion, implying that demand response has a risk-reduction value in addition
to its expected-value efficiency benefit.

######  Result 3.

Risk aversion has the largest impact on the overall system for low and
intermediate levels of demand flexibility. If demand is highly flexible, the
overall need for capacity – and consequently the investment risk – is reduced,
so levels of risk are also low. If demand is inflexible, investment is driven
purely by peak-load hours rather than by uncertain operating costs, so risk
aversion also has a smaller effect on optimal decisions.

In this section, we investigate the impact of demand response on an
electricity system with different levels of risk aversion. Aiming to isolate
the effect of demand responsiveness, we create a European merit order of load
shedding potential. As described above, we (i) average the sector-specific
costs provided by [5] and (ii) couple the resulting load shedding cost with
sector-specific shares of electricity consumption for each country.

In this analysis, we model four settings:

  1. (1)

_No demand responsiveness_ : demand is inelastic and load shedding is not
possible.

  2. (2)

_Low demand responsiveness_ : load shedding is possible at high costs. The
cost values of the merit order for load shedding are increased by a factor of
five.

  3. (3)

_Intermediate demand responsiveness_ : load shedding is possible at estimated
costs. The cost values of the merit order for load shedding are not scaled.

  4. (4)

_High demand responsiveness_ : load shedding is possible at low costs. The
cost values of the merit order for load shedding are halved.

In Table 1, we list the defined model settings and show the resulting ex-post
expected total system costs and European load shedding activities. Naturally,
a system with no demand responsiveness has the highest ex-post expected total
system cost. When demand responsiveness increases from low to high, we observe
decreasing costs. The differences quantify the value of the additional demand
responsiveness. For all four settings, ex-post expected total system costs
increase with risk aversion. This increase is a result of the nonzero cost of
risk mitigation.

Table 1 also lists the aggregated quantities of European load shedding
activities. In the ‘no demand responsiveness’ setting, shedding does not occur
and the system invests in enough generation capacity to satisfy peak net
demand in all scenarios. With increasing demand responsiveness, more shedding
occurs. However, the increasing load shedding does not lead to certain sectors
being permanently shut down. At its maximum, the proportion of hours in a year
in which load shedding occurs ranges from 1.7% in Sweden and Norway to 17.4%
in the UK.

Note also that shedding activities increase at higher risk-aversion levels –
that is, risk-averse decision-makers use the load shedding option to mitigate
risk. However, the relative increase in load shedding activities from risk-
neutral to risk-averse system planning differs across demand responsiveness
settings. The increase is stronger for the low and intermediate levels (88%
and 84%, respectively) compared to high demand responsiveness (30%). This
result illustrates that risk aversion has the largest impact on the energy
system for intermediate levels of demand flexibility.

Table 1. Ex-post expectation of total system costs at different levels of demand elasticity in bn. € and aggregated European load shedding activities in GWh |  $\omega\textsubscript{1}$=0 |  $\omega\textsubscript{2}$=0.2 |  $\omega\textsubscript{3}$=0.4 |  $\omega\textsubscript{4}$=0.6 |  $\omega\textsubscript{5}$=0.8 |  $\omega\textsubscript{6}$=0.99
---|---|---|---|---|---|---
[1] no demand responsiveness | 186.9 | 187.2 | 187.3 | 187.3 | 187.5 | 189.4
[2] low demand responsiveness | 186.4 | 186.6 | 186.7 | 186.8 | 186.9 | 188.6
[3] intermediate demand responsiveness | 184.3 | 184.5 | 184.6 | 184.8 | 186.8 | 187.0
[4] high demand responsiveness | 183.2 | 183.4 | 183.5 | 183.6 | 183.8 | 185.6
Load shedding at [1] | - | - | - | - | - | -
Load shedding at [2] | 563 | 657 | 810 | 908 | 1,005 | 1,059
Load shedding at [3] | 6,031 | 6,703 | 7,191 | 8,144 | 8,851 | 11,084
Load shedding at [4] | 17,200 | 17,954 | 18,399 | 18,949 | 19,903 | 22,277

####  5.2.2. The isolated effect of trade

######  Result 4.

Cross-border transmission capacity expansion has a higher value for risk
mitigation when decision-makers are risk averse.

######  Result 5.

Investment in cross-border capacity additional to the ENTSO-E TYNDP expansion
plan has a negligible impact on the ex-post expected total system costs. This
result, at least from the perspective of energy trading, indicates that the
existing system, in combination with the currently planned expansions, can
theoretically achieve most of the efficiency gains of cross-border trading if
this trading is frictionless.

In this section, we investigate the impact of trade within an energy system
with different levels of risk aversion. Hourly demand and renewable generation
patterns vary between European countries. In times of low residual load (i.e.
when supply is not scarce), free production capacities can be exported to
neighbouring markets. In times of high residual load (i.e. when supply is
scarce), electricity can be imported from neighbouring markets. Thus, trade
ensures the efficient utilisation of generation capacities. However, both
importing and exporting electricity require available transmission capacity
between markets. Hence, increasing transmission capacity increases system
flexibility.

In this analysis, we model three settings:

  1. (1)

_No endogenous NTC expansion_ : The TYNDP expansion plan is implemented in
full, but further endogenous transmission expansion is not possible.

  2. (2)

_Endogenous NTC expansion_ : Further endogenous transmission expansion is
possible at the current CAPEX estimate.

  3. (3)

_Endogenous NTC expansion at reduced costs_ : Further endogenous transmission
expansion is possible at 50% of the current CAPEX estimate.

Note that the TYNDP expansion plan for 2030 is implemented exogenously in all
three settings. Hence, the NTC investments derived from the model are to be
understood as additional to the current expansion plan. For example, the 50%
CAPEX assumption in the third setting can be seen as the result of political
efforts to intensively interconnect European energy markets.

Table 2 depicts the ex-post expected total system costs and selected
transmission capacities. It reveals several insights into the role of cross-
border energy trade in risk-averse planning.

First, although the value of additional investments in cross-border capacity
is non-negative in our model setup, we find that the actual changes in ex-post
expected total system costs are small (columns in Table 2). This result
indicates that the currently planned system can theoretically achieve most of
the efficiency gains of cross-border trading, assuming that this trading is
frictionless. Naturally, cross-border transmission has additional benefits
beyond straightforward arbitrage, which we do not consider here.

Second, both the ex-post expected total system costs and the investment
quantities increase with higher levels of risk aversion in all three settings
(rows in Table 2). The positive correlation between invested capacity and
risk-aversion levels indicates that flexibility from transmission expansion
has a higher value for risk-averse system planning; its deployment for risk
mitigation increases with risk aversion.

Overall, an interconnected energy system aims to exploit synergies between the
residual load patterns in different nodes and to optimise the utilisation of
generation capacities. Since risk-averse planning does not address uncertainty
in peak demand by increasing installed generation capacities (see 5.1),
efficient capacity utilisation is especially important. This drives the need
for additional transmission capacity, which strengthens the interconnection
across Europe. A detailed list of newly build interconnectors is presented in
Appendix C.

Table 2. Ex-post expectation of total system costs with and without the possibility of trading electricity and building interconnectors in bn. € and endogenous investments in transfer capacities in MW |  $\omega\textsubscript{1}$=0 |  $\omega\textsubscript{2}$=0.2 |  $\omega\textsubscript{3}$=0.4 |  $\omega\textsubscript{4}$=0.6 |  $\omega\textsubscript{5}$=0.8 |  $\omega\textsubscript{6}$=0.99
---|---|---|---|---|---|---
[1] no endogenous NTC expansion | 186.9 | 187.2 | 187.3 | 187.3 | 187.5 | 189.4
[2] endogenous NTC expansion | 186.9 | 187.1 | 187.2 | 187.4 | 187.7 | 188.4
[3] endogenous NTC expansion at reduced costs | 186.7 | 187.0 | 187.1 | 187.3 | 187.3 | 188.0
Endogenous NTC investments at [2] | 6,459 | 7,447 | 8,763 | 10,214 | 14,586 | 15,601
Endogenous NTC investments at [3] | 15,479 | 15,107 | 17,021 | 24,402 | 26,086 | 27,789

####  5.2.3. The isolated effect of energy storage

######  Result 6.

Like demand response and cross-border trading, the value of storage increases
with the level of risk aversion in the market.

In this section, we investigate the impact of energy storage on systems with
different risk-aversion levels.

Storage units withdrawal electricity from the system at a certain point in
time and re-inject it at any later point, reduced by efficiency losses. Thus,
storage provides the flexibility needed to reduce imbalances between supply
and demand. While energy storage technology has various forms, we focus
exclusively on pumped-storage plants (PSPs) to avoid unnecessary complexity.

In this analysis, we model three settings:

  1. (1)

_No endogenous PSP expansion_ : Endogenous storage expansion is not possible.

  2. (2)

_Endogenous PSP expansion_ : Endogenous storage expansion is possible at the
current CAPEX estimate.

  3. (3)

_Endogenous PSP expansion at reduced costs_ : Endogenous storage expansion is
possible at 50% of the current CAPEX estimate.

Note that the existing storage capacities are present in all three settings.
Hence, PSP investments derived from the model are to be understood as an
extension of currently installed capacities. Similar to the assumption made in
section 5.2.2, a 50% CAPEX setting could be interpreted as a future in which
an increased political effort is made to promote storage investment in Europe;
it could also simply be a result of unexpected technological progress.

Table 3 reports the ex-post expected total system costs and realised storage
investments. First, we find a minor decrease in ex-post expected total system
costs as the availability of storage investments increases (columns in Table
3).

Second, we observe no storage investments at current cost levels (row $[2]$),
which means that the price spread between base and peak times does not
compensate for additional storage investments. Note, however, that we do not
consider any revenue streams for storage except for the energy-only market. In
the reduced CAPEX scenario (row $[3]$), we observe significant storage
investments.

Third, the quantity of storage investments follows an interesting pattern
under different levels of risk aversion. Storage investments remain constant
for the first three steps
($\omega\textsubscript{1}--\omega\textsubscript{3}$); the investments increase
at higher values of risk aversion. At lower levels of risk aversion (and
indeed, in the risk-neutral setting), the entire potential storage capacity in
France and the Iberian Peninsula is exploited; these regions have high price
spreads because of the composition of the local generation mix. Only if risk
aversion is high enough to overcome the significant costs of PSPs further
investments are made in Belgium.

Table 3. Ex-post total system costs with and without the option to invest in storage in bn. € and PSP investments in MW |  $\omega\textsubscript{1}$=0 |  $\omega\textsubscript{2}$=0.2 |  $\omega\textsubscript{3}$=0.4 |  $\omega\textsubscript{4}$=0.6 |  $\omega\textsubscript{5}$=0.8 |  $\omega\textsubscript{6}$=0.99
---|---|---|---|---|---|---
[1] no endogenous PSP expansion | 186.9 | 187.2 | 187.3 | 187.3 | 187.5 | 189.4
[2] endogenous PSP expansion | 186.9 | 187.2 | 187.3 | 187.3 | 187.4 | 189.1
[3] endogenous PSP expansion at reduced costs | 186.8 | 187.0 | 187.1 | 187.2 | 187.4 | 188.1
PSP investments at [2] | - | - | - | - | - | -
PSP investments at [3] | 15,964 | 15,964 | 15,964 | 15,964 | 16,358 | 17,256

####  5.2.4. Interplay of flexibility elements

######  Result 7.

Different sources of flexibility can be complements or substitutes depending
on the level of risk aversion.

In the following section, we analyse the interplay of flexibility elements
under different risk-aversion levels. This is done by including all three
flexibility elements in the model’s formulation. In this analysis, we apply
two settings that differ with respect to system flexibility:

  1. (1)

_Moderately flexible system_ : includes the European merit order for load
shedding, as well as the options to invest in NTCs and storage at current cost
levels.

  2. (2)

_Highly flexible system_ : replicates the setting above, but cost levels are
reduced by 50%. Thus, we combine ‘flexible’ settings from sections
5.2.1–5.2.3.

Table 4 shows the results for the _moderately flexible system_ setting. This
table depicts the utilisation of the three flexibility elements under
different risk-aversion levels (rows 1–3) and the differences between these
values and the values observed in sections that consider respective
flexibility elements in isolation (5.2.1–5.2.3, rows 4–6). Hence, a negative
value in the ‘Delta load shedding [GWh]’ row indicates a decrease in load
shedding in a setting if all three elements are available. Conversely, a
positive value indicates an increase. Similarly, Table 5 presents the results
for the _highly flexible system_ setting.

In the _moderately flexible system_ , load shedding activities and NTC
investments increase with higher risk aversion, but storage facilities are not
built. However, the delta rows show small differences in utilisation for the
flexibility elements (i.e. load shedding volumes and investments in NTCs and
storage) when compared to settings in which each element is implemented in
isolation. Hence, although the different flexibility elements are substitutes
or complements at different levels of risk aversion, these effects are very
small and exhibit no clear patterns

In the _highly flexible system_ , the picture is different. Load shedding
activities increase moderately at higher values of risk aversion. The
investments in NTCs increase remarkably from 19.3 to 53.7 GW. In contrast, the
investments in PSPs decline from 1.5 to 0 GW with higher risk aversion. When
compared to model settings with isolated flexibility elements, this analysis
shows significant differences. In particular, (i) PSP investments are
significantly lower, (ii) load shedding activities increase moderately at
lower levels of risk aversion but considerably decline when risk aversion is
high and (iii) investments in NTCs are always higher than in model settings
with isolated flexibility elements and increase progressively with higher
levels of risk aversion.

This result implies that transmission expansion becomes the dominant
flexibility element when the three elements are modelled together, in
particular when system planners are more risk averse. In such a setting,
storage units are no longer an efficient option to mitigate risk,
independently of the risk preference. In general, flexibility options can be
complements at low levels of risk aversion and substitutes at high levels, as
is the case with energy storage here.

Table 4. Utilisation of flexibility elements as the difference between a moderately flexible system and the system with the respective isolated element in 5.2.1 – 5.2.3 |  $\omega\textsubscript{1}$=0 |  $\omega\textsubscript{2}$=0.2 |  $\omega\textsubscript{3}$=0.4 |  $\omega\textsubscript{4}$=0.6 |  $\omega\textsubscript{5}$=0.8 |  $\omega\textsubscript{6}$=0.99
---|---|---|---|---|---|---
Aggregated load shedding [GWh] | 5,946 | 6,701 | 7,165 | 8,093 | 8,884 | 11,299
Endogenous NTC investments [MW] | 6,722 | 7,521 | 8,925 | 9,813 | 11,866 | 15,639
Endogenous PSP investments [MW] | - | - | - | - | - | -
Delta load shedding [GWh] | -85 | -1 | -26 | -51 | 32 | 215
Delta NTC investments [MW] | 263 | 74 | 162 | -401 | -2,720 | 38
Delta PSP investments [MW] | - | - | - | - | - | -
Table 5. Utilisation of flexibility elements as the difference between a highly flexible system and the system with the respective isolated element 5.2.1 – 5.2.3 |  $\omega\textsubscript{1}$=0 |  $\omega\textsubscript{2}$=0.2 |  $\omega\textsubscript{3}$=0.4 |  $\omega\textsubscript{4}$=0.6 |  $\omega\textsubscript{5}$=0.8 |  $\omega\textsubscript{6}$=0.99
---|---|---|---|---|---|---
Aggregated load shedding [GWh] | 17,851 | 18,375 | 18,748 | 19,027 | 19,001 | 19,451
Endogenous NTC investments [MW] | 19,257 | 18,658 | 21,346 | 30.040 | 39,901 | 53,718
Endogenous PSP investments [MW] | 1,476 | 2,026 | 1,571 | 594 | 98 | -
Delta load shedding [GWh] | 651 | 421 | 349 | 78 | -902 | -2,826
Delta NTC investments [MW] | 3,778 | 3,551 | 4,325 | 5,638 | 13,815 | 25,929
Delta PSP investments [MW] | -14,488 | -13,938 | -14,393 | -15,370 | -16,260 | -17,256

##  6\. Discussion

The above results show several interesting effects. First of all, we find that
risk aversion has a minimal effect on overall investment in electricity
generation capacity but increases investments in low-carbon capacity. This is
in line with the previous literature (e.g. [24]), but since we have taken
renewable investment to be exogenous, the increase applies mostly to nuclear
capacity. In particular, investing in nuclear generation capacity is not
optimal under a strictly risk-neutral objective but is only selected if market
participants are assumed to be risk averse. This finding shows that nuclear
generation capacity has additional value in mitigating risk despite its high
costs. It may also help to explain why countries such as the UK are actively
pursuing new nuclear investments even though they appear to be a sub-optimal
solution from a cost-based perspective. Finally, these results suggest that
estimates of endogenous renewable investments in the previous literature have
not unduly under- or overstated the effects of risk aversion.

The reason that low-carbon capacity is especially attractive to risk-averse
planners is, of course, the fact that CO2 price uncertainty is both the single
largest uncertainty in our model and the costliest to hedge against. Again,
this is consistent with previous findings. Our results illustrate that
policymakers must consider risk aversion in order to accurately predict the
impact of policy measures such as carbon markets. In addition, when sets of
scenarios are being generated, considerable attention is normally paid to
their internal consistency based on estimated or perceived correlations
between uncertain parameters. This can cause unexpected results when these
scenarios are used for, for example, long-term system planning. In particular,
if high-impact uncertainties correlate negatively with low-impact
uncertainties, low-impact uncertainties can appear to have the opposite impact
on model outcomes than what their isolated impact would be. Any type of
scenario-based work should consider this effect. In general, it is well-known
that the outcomes of stochastic planning models depend to a great extent on
the most extreme scenarios; in our case, the outcomes of risk-averse planning
models depend to a great extent on the scenarios that are costliest to
mitigate.

As expected, flexibility elements have more value in a risk-averse world; in
other words, risk aversion has less impact in a flexible electricity system.
This is good news for developers of flexible technologies because it implies
that the risk-neutral models that have often been used to evaluate new
investments have understated their benefits. Nonetheless, the results should
also encourage more analysis of risk.

However, flexibility options are not equal. Demand response, which can reduce
demand, more effectively reduces risk than technologies that only shift demand
in space or time, such as transmission or storage. Therefore, demand response
has long-term risk-reduction value in addition to short-term flexibility and
operational efficiency. In most current electricity markets, consumers have a
very limited ability to signal their willingness and adjust their demand; our
results provide all the more reason to change this.

This is particularly important in the medium term since there are (perhaps
counterintuitively) nonlinearities in the relationship between flexibility and
risk. In particular, the effects of risk are most pronounced at medium levels
of demand flexibility. This occurs because, in a very inflexible system,
generation investment is driven by the highest level of demand. As a result,
the utilisation factors of peak-load capacity are low, and uncertainty about
their marginal costs is less important. In a highly flexible system, less
overall capacity is necessary, which also reduces risk. This implies that, in
the energy transition, the coming decade will perhaps see the highest level of
risk and the largest impact of risk aversion. This means that financial
markets and other methods to mitigate or hedge risk are more important now
than ever and that further investments in flexibility elements will have
significant benefits.

Our results also show interesting interactions between flexibility elements.
At the current cost levels for flexibility and for all risk-aversion levels,
our results do not show synergies or substitution effects that significantly
affect shedding activities or decisions about investment in transmission or
storage capacity. However, this picture changes significantly when flexibility
options become cheaper. Transmission expansion becomes the dominant
flexibility element, replacing storage investments in particular, and this
effect increases with higher risk aversion. This means that in future
electricity markets, flexibility provided by efficient electricity trading
will create more system value than ever. This value is realised through
arbitrage opportunities across time and space to the extent permitted by the
transmission infrastructure. This effect creates a system benefit of further
integration of the current European energy system and supports additional
research on improving transmission infrastructure. On the contrary, risk-
averse system planners will most likely not make additional storage capacity
investments if they are optimising arbitrage revenues alone. Despite political
efforts, this could inhibit both the expansion of storage technologies and the
development of storable energy carriers, such as hydrogen.

Naturally, our approach has limitations. First, we use a linear model that
assumes completeness and perfect competition in both electricity and financial
markets and does not include some of the nonlinearities that are present in
real-world power system operations. In reality, incomplete financial markets
will lead to an inefficient distribution of risk among market participants,
increasing the cost of uncertainty and the effects of risk aversion. Moreover,
nonlinearities in power plant operations can increase the need for flexible
generation capacity, possibly reducing the amount of nuclear energy in an
optimal generation mix.

Second, our operationalisation of demand response, which is based on published
values of lost adequacy, is a very rough approximation of real demand response
potential and cost. Likewise, our NTC-based approach to transmission and
transmission investment only approximates real-world network constraints and
investment opportunities.

Third, we only consider the value of generation capacity and flexibility
elements in the electricity market. Naturally, most of these technologies and
options have value in other applications, including ancillary services markets
and secure power systems operation. Indeed, the current storage capacity in
Europe derives a large part of its revenue from non-electricity services.

Finally, as in all stochastic risk-averse models, our results depend to a
large extent on the scenarios we have used. Scenarios are subjective by
definition and any set of scenarios describes only a limited range of possible
futures. Our study is based on the TYNDP scenarios, which are a widely
consulted and used set of scenarios that we consider representative of the
scenarios that actual decision-makers use; in a Bayesian sense, they are
therefore one of the best subjective scenario sets. However, individual
decision-makers will use different scenarios with different probabilities,
which we cannot capture.

All of this means that our quantitative results may vary with model
assumptions and parameters. Nevertheless, we expect our qualitative results to
carry over to a wide range of model formulations and, indeed, to the real
world. In particular, our qualitative results demonstrate the interplay
between investment risk and flexibility. This is clearly an important
dimension of energy systems planning and modelling that should receive
increased attention in future research.

##  7\. Conclusion

In this paper, we investigate risk-averse decision-making in the context of
long-term system planning. We develop a pan-European stochastic electricity
market model that accounts for the risk-averse decision-making behaviour of
its agents. We apply a set of risk-aversion levels and analyse 1) the impact
of risk aversion on investments and 2) the use of flexibility options
including demand response, storage and interconnection in such a system. In
doing so, we generalise the literature on risk-averse planning to a setting
that much more closely resembles future, flexible electricity markets. We also
generalise the literature on the value of flexibility to settings where
planners are risk-averse.

We find that risk aversion decreases investment incentives, especially for
high-emission technologies. However, since risk-averse decision-makers
consider all uncertainties in combination such that these uncertainties
correlate with each other and have a different level of impact, we observe
counterintuitive effects. In particular, we show that risk aversion does not
lead to an overall increase in capacity investment despite the presence of
demand uncertainty.

Although we implement a variety of parameters that are subject to uncertainty,
we find that in the European context, carbon price uncertainty generates the
highest investment risk. Hence, as risk aversion increases, we see a shift in
the investment mix from emission-intensive to emission-free technologies. This
may explain why some countries are actively pursuing new nuclear investments
even though this appears to be sub-optimal from a cost-based perspective.

Furthermore, we find that flexible technologies have a higher value for risk-
averse decision-makers – that is, mitigating risk is easier in a flexible
electricity system. This implies that models that use risk neutrality as a
central assumption, which have often been used to evaluate investment
decisions, have underestimated the benefits of system flexibility. However,
the impacts of risk are nonlinear; we observe an especially large impact of
risk aversion on model outcomes for intermediate levels of flexibility.

Finally, we investigate the interplay between the flexibility elements. At the
current cost levels for flexibility and for all risk-aversion levels, our
results do not reveal significant synergies or substitution effects among
flexibility elements. However, once flexibility is available at lower cost,
transmission expansion becomes the dominant flexibility element, replacing
storage investments; this effect increases at higher levels of risk aversion.

Further research on this topic is necessary and could address the limitations
discussed above. Our model is formulated as a linear cost minimisation problem
and considers demand flexibility only with the value of lack of adequacy.
Future studies could form a nonlinear welfare maximisation problem that allows
a more detailed representation of demand elasticity. Research on the extent to
which nonlinearities in power plant operation increase the need for
flexibility could also provide new and interesting insights. Finally, further
analysis could extend the time period considered in this study to map the
transformation of the European energy system to 2050 and beyond.

## Acknowledgements

A.H. van der Weijde received support from the Alexander von Humboldt
Foundation through a Humboldt Fellowship. Thomas Möbius received support
through the research project ProKoMo, which is funded by the German Federal
Ministry of Economic Affairs. Iegor Riepin received support through the
research project Ariadne (Kopernikus project), which is funded by the German
Federal Ministry of Education and Research.

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## Appendix

Appendix A: Scenario Data

Table 6. Projections for installed RES capacities in GW Table 7. Fuel and CO2
prices. Monetary values are in €${{}_{2}015}$ Table 8. Characteristic demand
levels in 2030 cumulative for all model regions in GWh

Appendix B: Geographical Scope

Below, we list the countries and regions included in our model’s geographical
scope. Note that the model structure consists of a network of nodes. A node
represents one country or a group of several countries from one region. The
geographical scope covers EU member states, European countries that are not
part of the EU. We elicit node names as defined by the two-letter ISO 3166
international standard. In cases where countries are represented by a compound
region with aggregated data, we set the node name in line with the name of the
region.

Table 9. Model regions

Appendix C: Supplementary Material

Table 10. Newly built NTCs in MW at currently estimated CAPEX Table 11. Newly
built NTCs in MW at 50% of current CAPEX