# How much flexibility is available for a just energy transition in Europe?

Tim T. Pedersen 111Department of Mechanical and Production Engineering, Aarhus
University, Aarhus, Denmark222ICLIMATE Interdisciplinary Centre for Climate
Change, Aarhus University, Aarhus, Denmark Mikael Skou Andersen 333Department
of Environmental Science - Environmental social science and geography, Aarhus
University, Foulum, Denmark44footnotemark: 4 Marta Victoria 555Department of
Mechanical and Production Engineering, Aarhus University, Aarhus,
Denmark666ICLIMATE Interdisciplinary Centre for Climate Change, Aarhus
University, Aarhus, Denmark Gorm B. Andresen 777Department of Mechanical and
Production Engineering, Aarhus University, Aarhus, Denmark888ICLIMATE
Interdisciplinary Centre for Climate Change, Aarhus University, Aarhus,
Denmark

###### Abstract

The transition of Europe’s energy supply towards carbon neutrality should be
efficient, fair, and fast. In principle, the efficiency of the transition is
ensured by the European Emissions Trading System (ETS), creating a common
emissions market. Fairness is aimed for with the Effort Sharing Regulation,
calibrated for the economic capacity of member states. These two pieces of
legislation are aiming for a trade-off between efficiency and fairness. A
Monte Carlo simulation with 30.000 samples of national reduction target
configurations has been performed using an advanced energy system optimization
model of electricity supply as of 2030. Results reveal a group of countries
where emissions reductions beyond the national targets, in most scenarios, are
economically favorable. Contrarily, for some countries large abatement costs
are unavoidable. Compared to the most cost-effective CO2 allocation, accepting
a moderate increase in cost enables alternative CO2 emissions allocations that
incorporate alternative justice-based distribution criteria.

###### keywords:

Energy justice , EU ETS , Energy System Optimization , Modeling to Generate
Alternatives ,

††journal: One Earth

Monte Carlo study of uncertain national emission reduction targets in EU

Moderate increases in total system cost reveal a large range of alternatives
to EU ETS

Strong anticorrelation of national emissions indicates carbon leakage given
inhomogeneous CO2 prices.

Countries where emissions are hard to reduce are likely to have high emission
intensities and power prices.

##  1 Introduction

The European Green Deal raises the ambition level for decarbonization of the
European energy sector, in combination with explicit aims to ensure a just
transition [1]. The quality of a just transition is, however, not easily
measured and has in recent years become a topic of much debate [2, 3].
Emissions from the energy sector are currently governed by the EU Emission
Trading System (EU ETS) [4], operating on the cap-and-trade principle,
requiring that all power generators in Europe buy emission allowances. The
Just Transition Mechanism combined with the Just Transition Fund is introduced
to ensure a more equitable transition [5]. Since 2013, a gradually declining
amount of emissions allowances has been auctioned off to power plants and
industrial emitters on an annual basis, hence setting a price on CO2 emissions
and providing an incentive to limit these [6]. By gradually lowering the
amount of allowances on auction year by year, the EU ETS determines the
overall rate of emissions reductions by EU Member States as a whole. The
annual reduction rate will be fixed in accordance with the recently agreed
commitment by the EU to reduce greenhouse gas emissions by 55% by 2030 [7].
The burden of reducing emissions is moreover allocated among EU member states
by setting national reduction targets. Emissions from sectors not covered by
the EU ETS are determined through the Effort Sharing Regulation [8],
translating the overall 55% reduction target into national targets for each
Member State. The national targets are based on Member States’ relative
wealth, measured by gross domestic product (GDP) per capita, to ensure a just
transition [8]. Still, some countries have unilateral reduction measures for
emissions not governed by the EU ETS, such as the Swedish carbon tax. These
measures may lead to carbon leakage [9] which may decrease overall welfare
[10].

The European power sector is on the verge of a major transformation from a
fossil-fuel-based system to rely mainly on renewable and low-carbon resources
[11]. However, the starting point differs widely, with some countries having
already high shares of carbon-neutral energy sources, while other countries
still are deeply reliant on fossil fuels [12]. The transformation of domestic
energy supply is challenged by several factors of technical, economic, and
political nature. The access to renewable resources [13], currently operating
power plants, and availability of international transmissions connections [14]
are some of the key technical parameters. Figure 1 a) shows the capacity of
plants installed today and expected to remain in operation by 2030. It is
clear, that the preconditions for rapid decarbonization are very diverse, with
some countries relying heavily on coal and oil, while others have a large pool
of renewable power generators. Figure 1 b) shows the potentials for renewables
per Member State. Renewable potentials are calculated as the geographical
potential for renewable capacity multiplied by the average national capacity
factor for the given renewable resource. It is evident that the renewable
potentials are unrelated to country size and energy demand. The vastly
different starting points of member states should be captured by the EU ETS
and the Effort Sharing Regulation [8] if a just transition is to be achieved.

Figure 1: Existing generator capacity and renewable potentials - a) Currently
installed technology capacity that will be in service in 2030. Capacities
represent maximum electricity generation. b) Effective renewable energy
potentials, calculated as the maximum geographical potential times the local
capacity factor for the given technology. Wind turbine capacity is specified
as offshore and onshore. Hydro-power is separated as either run-of-river
(ROR), pumped-hydro-storage (PHS), or hydro. Two types of gas turbines are
included. These closed-cycle-gas-turbines (CCGT) and open-cycle-gas-turbines
(OCGT). Transmission capacities are indicated either as high voltage AC or DC
transmissions lines. The majority of countries have both brownfield and
renewable potentials to cover several times their annual electricity demand.

A uniform CO2 price is said to be the most efficient way to achieve emissions
reductions [10]. However, with the uniform CO2 price, the fairness of the
transformation cannot be ensured. Allocating the global carbon budget to
ensure fairness is, however, a daunting task with many possible outcomes. Zhou
and Wang [15] identify a range of allocation schemes, based on different
principles, such as sovereignty, egalitarianism, efficiency, horizontal
equity, vertical equity, and polluter pays. Other studies combine these
principles to create more complex allocation schemes, such as the Model of
Climate Justice per capita [16], where historical emissions along with
population growth are considered. Choosing a single right allocation scheme is
inherently difficult as it is not a question about costs but rather one of
ethics [17]. Markowitz notes that we are ill-equipped to decide, given the
complexity of the problem, and our own complicity in causing it [18]. Still,
Jenkins et. al. identify three core tenets of energy justice: Distributional,
recognition, and procedural [2]. Distributional justice recognizes the unequal
distribution of environmental benefits and provides the rationale for this
research. Recognition justice states that individuals must be fairly
represented and have equal rights, whereas procedural justice concerns access
to the decision-making process. Only distributional justice will be considered
in this work.

Schwenk-Nebbe and co-authors [19], consider three different allocation
principles for establishing national CO2 reduction targets in a European
context that are of interest here. In their paper, emissions are allocated
based on cost efficiency, sovereignty (local-load) and, grandfathering
(local-1990). The efficiency scenario applies a uniform CO2 price, the
sovereignty scenario allocates emissions proportional to national electricity
demand, and the grandfathering scenario allocates on the principle of
historical emissions. In their analysis, Schwenk-Nebbe et al. find that with
the Efficiency solution, remaining emissions will be concentrated in a small
number of countries where the costs of decarbonization are highest. Allocating
emissions after the Sovereignty or Grandfathering principle respectively will
distribute remaining emissions more evenly while implying a spread in unit
abatement costs and higher total system cost. Bauer et al. [20] studied the
trade-off to be made between economic efficiency and sovereignty in a global
context using a multi-objective approach. Their findings indicate a highly
non-linear trade-off between efficiency and sovereignty, where the
intermediate scenarios can secure higher total benefits. The studies by
Schwenk-Nebbe and Bauer [19, 20] do, however, only analyze a fraction of the
possible ways national CO2 reduction targets can be distributed. As found in
[15], there are numerous allocation approaches resulting in a vast number of
emission allocations. The aim of this work is to identify the entire range of
possible configurations, to reveal the scale of flexibility available and the
associated cost of deviating from a uniform CO2 price.

In this research, a Markov Chain Monte Carlo (MCMC) method [21] has been
employed in combination with a techno-economic optimization model of the
European power supply system to identify and study all the possible
configurations of national reduction targets. By identifying all possible
configurations, the flexibility available for achieving a just transition can
be quantified and possible challenges can be pointed out. The reduction
allocation configurations are represented each with a unique set of national
reduction targets for all of the modeled countries. Two criteria are required
for all the configurations. First, a joint CO2 reduction of at least 55% must
be achieved by the model countries according to the EU’s 2030 Climate Target
Plan [7]. Second, the total system cost of implementing the reduction targets
must not increase by more than 18% relative to the cost-optimal allocation of
targets. This constraint is based on the principles from Modeling to Generate
Alternatives (MGA) where economically near-optimal model solutions are studied
[22]. Applying MGA methods to energy system optimization models has gained a
lot of attention recently [23, 24]. MGA has, however, mainly been used to
study technical flexibility among the near-optimal solutions [25]. The method
employed in this work consists of two steps. First, using an MCMC method to
devise a random set of national CO2 reduction targets for the model countries.
Second, the total system costs and the realized emission of the reduction
configurations are then evaluated using an energy system optimization model.
If the reduction target configuration satisfies the two aforementioned
criteria, it is accepted and stored. If not, the outcome is rejected. This
process is iterated until sufficient sample size is obtained. The result is a
huge set of configurations of national reduction targets comprising all
potential configurations satisfying both criteria.

The novelty of this work lies in the combination of a power system
optimization model and MCMC methods to study the possible configurations of
national reduction targets in a European context. Where previous studies have
used scenario-based modeling or multi-objective optimization to study a small
range of possible solutions, the method applied in this work is capable of
identifying a much larger range of possible outcomes. Furthermore, detailed
information about each configuration of national reduction targets can be
obtained, as the power system optimization model is solved for each allocation
scheme.

##  2 Methodology

The aim of this paper is to analyze the implications of different potential
allocations of the national reduction targets and their effects on the
European power system. The criteria listed in Table 1 indicate which
configurations can be considered feasible. In addition to the criteria already
discussed above, it is required that national level emissions of each Member
State must not surpass the equivalent of supplying 150% of their domestic
demand with coal power, i.e. becoming a super exporter of fossil-fuel-based
electricity. Such scenarios are considered highly unrealistic in light of the
European Green Deal.

Table 1: CO2 configurations scheme feasibility criteria a) |  The joint CO2 reductions must be equal to or greater than 55% relative to 1990.
---|---
b) |  Total system cost of the configuration of national reductions should not exceed the cost-optimal scenario with 18%.
c) |  A technically feasible solution to the model exists.
d) |  National emissions must remain below the equivalent of supplying 150% of energy demand with coal.

To identify the possible reduction target configurations, a modified version
of the Adaptive Metropolis-Hastings (AMH) sampler is used [21]. The sampler
falls under the broad umbrella of MCMC samplers. By using the AMH sampler to
efficiently sample possible configurations of national reduction targets,
while rejecting configurations considered infeasible, it is possible to
approximate the overall distribution of the feasible reduction configurations.
The sampled variables are the national CO2 reduction targets for the model
countries. Using the AMH sampler, distributions approximating the
distributions of all feasible configurations of national reduction targets are
obtained. A detailed description of the sampler is available in B.

Next, the sampled configurations of national reduction targets are evaluated
using an energy system optimization model of the European power sector. The
model uses the PyPSA-Eur-Sec framework [26] to define a model spanning 33
ENTSO-E (European Network of Transmission System Operators for Electricity)
member countries, i.e. the model includes EU-27 without Cyprus and Malta,
along with Norway, Switzerland, Serbia, Bosnia-Herzegovina, Albania,
Montenegro, Macedonia and, United Kingdom. The model assumes long-term market
equilibrium as well as perfect competition and foresight. A 2030 brownfield
scenario is modeled, where all installed generator capacities as of 2019 that
are expected to be in operation in 2030 are included. To cover energy demands,
the model will install new generation capacity, where it is economically
optimal. The model uses a one node per synchronous zone setup, with the nodes
connected by high voltage AC and DC lines. Using one year of energy demand and
weather data resolved in 3-hour time-steps, the model determines the cost-
optimal dispatch, power flows, and investment in new generator capacity.
Transmission line capacities included in the model are the currently installed
capacities, plus the planned capacities from the Ten Year Network Development
Plan (TYNDP 2018) [27]. The energy-generating technologies included are hydro,
onshore wind, offshore wind, solar PV, CCGT, OCGT, coal, lignite, nuclear, and
oil. Furthermore, two storage technologies are included. These are hydrogen
and battery storage. The technology parameters are listed in Appendix Table 4.
Brownfield capacities are shown in Figure 1 and in Table 5. The national CO2
reduction targets provided by the AMH sampler are included as constraints in
the model, limiting CO2 emissions from energy generation in each of the
modeled countries. Still, modeled countries are free to over-perform on the
national CO2 reduction target if it is economically favorable.

Technology cost predictions for 2030 are used for all expandable generator
types. Data for technology costs are indicated in Appendix Table 3. 2013 is
chosen as the meteorological reference year, as the hourly demand and weather
profile is a good representation of an average year. A single model evaluation
can be completed in approximately 15 minutes on a 4 core machine with
sufficient memory. Solving the optimization problem 30.000 times, requiring 15
minutes each, was performed using 10 parallel threads, resulting in roughly 30
days of computation.

By evaluating the results of the energy system optimization model for a given
configuration of national reduction targets, it is possible to determine
whether the configuration satisfies all criteria of Table 1. Each
configuration can then be accepted or rejected based on the result.

Table 2: Strategies for CO2 target configurations Name |  Interpretation |  Rule
---|---|---
Grandfathering |  All nations have equal right to pollute |  Distribute emissions proportionally to historical emissions
Sovereignty |  All nations have equal right to pollute |  Distribute emissions proportionally to energy demand
Efficiency |  Maximize global welfare |  Distribute emissions to reduce total socio-economic costs
Egalitarianism |  All citizens have equal right to pollute |  Distribute emissions proportionally to population size
Ability to pay |  Nations with higher welfare should take on a larger part of the task |  Distribute emissions inversely to GDP per capita

###  2.1 Methodology limitations

Weather and demand patterns are expected to change as a result of global
warming and general electrification of energy use. Investigating these effects
is, however, beyond the scope of this paper. Only the electricity sector has
been modeled. At a European level, the effects of sector coupling are only
expected to be moderate by 2030, thus, this simplification is believed to
provide only a minor source of error. If sector coupling was implemented, the
electricity sector could be expected to achieve a higher decarbonization rate
than involved with the 55% target, as it is considered easier to achieve here
than in other sectors.

##  3 Results

Five principles for allocation of national reduction targets are of interest
here. Based on section 2, these are grandfathering, sovereignty, efficiency,
egalitarianism, and ability to pay. The procedures for the allocation of
national reduction targets, and conversely the emissions, for each of these
five principles, are shown in Table 2. Using these five principles, six
emission reduction configurations have been created as seen in Supplementary
Figure 8. The Efficiency 55% and Efficiency 70%, configurations correspond to
using EU ETS at 55 and 70% joint reductions respectively, whereas, the
Grandfathering, Sovereignty, Egalitarianism and, Ability to pay configurations
represent alternatives to EU ETS. These configuration principles are
implemented such that they all distribute the same CO2 budget, except for the
efficiency 70% reduction configuration. As allowable emissions are left unused
by some countries, as they find it economically favorable to do so, the total
realized CO2 reduction for all configuration principles other than Efficiency,
will be higher than the minimum goal of 55%. The configuration principles
could alternatively be implemented to all have realized emissions
corresponding to a 55% CO2 reduction. A choice was made to use configurations
with equal CO2 budgets rather than equal realized emissions, as they represent
a more diverse set of scenarios and better represent a decision process where
budgets are allocated as national targets that will be realized, e.g. a decade
later. For results using configurations with equal realized emissions see D.

Applying the described MCMC method, a total of 30.000 random configurations
were drawn, with an acceptance rate of $\approx 80\%$. All samples were saved
allowing for analysis of emitted CO2, technology investments, and electricity
prices.

In Figure 2, the resulting realized CO2 emissions from all configurations of
national reduction target allocations is shown, plotted against their total
system costs. The reference scenario (Efficiency) with the lowest total system
cost is indicated with the red cross. The Pareto optimal front was calculated
by continuously decreasing the targeted joint CO2 emissions and is indicated
by the blue line.

Figure 2: Distribution of possible CO2 reduction configurations - Histogram
showing the CO2 reductions relative to 1990 and the associated costs of all
feasible configurations of national reduction targets. The minimum required
CO2 reduction and maximum allowable cost increase is marked with red lines.
The blue line marks the Pareto-optimal front of a dual objective optimization
procedure using total system cost and joint CO2 reduction as the two objective
functions. The reduction target scenarios Efficiency 55%, Efficiency 70%
Grandfathering, Ability-to-pay, Egalitarianism, and Sovereignty are marked
with orange.

In the figure, a gap between the Pareto optimal front and the actual outcomes
can be observed. There is nothing preventing the sampler from identifying
configurations on the Pareto optimal front, it is, however, very unlikely. The
probability of the sampler drawing the exact combination of the 33 variables
that will lead to a Pareto optimal solution is very low. This also shows that
the optimal solution is an extreme scenario that is very hard to obtain
without extensive collaboration and agreement between all model countries.
This is very unlikely, as countries have individual national targets and
agendas. Therefore, we argue that solutions located in the dark blue regions
of Figure 2 can be considered as significantly more probable outcomes because
they can be realized with many different configurations of national reduction
targets.

All the allocation principles, except Efficiency 55%, are seen to provide a
higher CO2 reduction than required. This over-performance on emissions
reduction is a result of several countries finding it cost-optimal to reduce
emissions beyond their assigned national target. In the Efficiency
configurations only a single common CO2 emission constraint is used. In all
other scenarios, national CO2 emission constraints apply. In scenarios with
realized reductions becoming higher than 55%, the national CO2 constraint is
not binding in one or more countries. The Grandfathering and Ability to pay
schemes are located relatively close to the Pareto-optimal front, whereas the
Sovereignty and Egalitarianism are found to be further from it (see Figure 2
and Figure 9). For the Grandfathering distribution, this makes sense
intuitively because countries with good renewable resources may already have
exploited them in the past.

Considering the distribution of the joint CO2 reduction, it is clear that the
probability of achieving reductions close to the joint target (marked by the
vertical red line) is more likely than overachieving. Moreover, the
distribution of the system costs reveals that an increase in the total system
costs of not less than 5% relative to the cost-optimal scenario is almost
unavoidable, since, to obtain the lowest possible total system costs, the
burden of transitioning must be shared in a very exact way. It is,
nevertheless, very unlikely that this will happen as countries have different
national ambitions. Therefore costs higher than what is deemed optimal is to
be expected. What Figure 2 also shows, is that this cost increase with a 75%
probability will be above 4.6% and it has a 50% probability of being between
4.6% and 12.2%.

Figure 3: National emission intensity - National CO2 emissions intensity for
all modeled scenarios. Emission intensity is measured as emitted CO2 pr MWh of
produced electricity. The scenarios Grandfathering, Sovereignty, Efficiency,
Egalitarianism, and Ability to pay is highlighted.

Figure 3 shows the probability range for CO2 intensity (emissions per MWh) in
each of the modeled countries according to the various configurations of
national reduction targets. As seen in the figure, all countries have zero
emissions in one or more configurations. Countries such as Norway and Sweden
have zero emissions under all circumstances. This is not because they are
allocated a demanding reduction target, but simply because it is cost-optimal
to rely fully on renewable or nuclear energy in these countries. On the other
hand, countries such as Poland and North Macedonia tend to have large
emissions intensity in most configurations (allocation schemes where these
countries have ambitious reduction targets are very likely to be rejected). By
analyzing the configuration of national reduction targets in the Efficiency
approaches, it can be observed that higher than average shares of emissions
are allocated to countries that at the outset have high emissions and less
than average shares of emissions are allocated to countries with low initial
emissions. In other words, the Efficiency schemes favor assigning modest
reduction targets to countries that have a hard time reducing emissions and
cutting emissions drastically in countries where CO2 reduction is easier. This
intuitively reduces total system cost. When comparing the Efficiency scenario
with 55% and 70% reductions, we can identify countries that are next in line
to reduce emissions such as the Netherlands, Italy, and Portugal, as they all
reduce emissions substantially in the 70% scenario. There are, however, also
countries where the emission intensity is undisturbed even though joint
emissions have been reduced. In the Sovereignty configuration, CO2 reduction
targets are assigned equally based on the national energy demand. Naturally, a
much more even emissions intensity results from this approach. Poland and the
Netherlands are, however, observed to have higher emission intensities than
the other countries. In the Ability to pay approach emissions are distributed
inversely proportional to national GDP per capita. This redistribution of
emissions with the Ability to pay approach is clearly discerned in Figure 3,
where wealthy countries such as Germany and the Netherlands end up with low
emissions while countries such as Romania, Macedonia, Poland, and Bulgaria
feature higher emissions.

Figure 4: Correlation of emissions - The data used to create this figure is
the Pearson correlation of the national CO2 emission across all samples. a)
CO2 emission correlations shown on a map of the model countries. Correlation
strength and direction is indicated by the link color and size. Correlations
below 0.2 has been removed for clarity. b) A matrix plot of CO2 emission
correlation for all model countries.

By analyzing the country correlations of actual national CO2 emissions
resulting from all the configurations, Figure 4 is generated. From Figure 4 a)
it is evident that for neighboring countries outcomes are closely linked. The
strong positive correlation between Sweden and Norway’s emissions is however
an artifact, as these two countries have zero emissions with almost all
approaches and configurations. Germany is found to play a key role in the
emission profiles of many central European countries. Strong negative
correlations are seen between Germany and the neighbors France, Austria,
Denmark, Luxembourg, and the Netherlands. This indicates that in accepted
configurations where Germany is assigned low emissions, the neighboring
countries are likely to experience higher than average emissions. A likely
explanation is that energy production, and thereby also emissions, are moved
from the country with tight national targets to countries with available
allowable emissions. This behavior is expected when inhomogeneous carbon
prices are enforced. The findings correlate well with the findings in [9],
where carbon leakage internally in Europe is identified as inhomogeneity of
carbon prices increases. A cluster of tightly correlated countries is,
furthermore, found among the Baltic Sea countries of Poland, Estonia,
Lithuania, and Latvia. Here Poland appears to be dominating, with strong
negative correlations to the three other countries. This reveals a dynamic
where CO2 emitting surplus moves between these countries depending on where
national emission reduction targets are tightened the most. In this region of
Europe renewable resources are low, especially in Poland, and the strong
correlation could indicate that the respective countries somehow are dependent
on a pool of potential but dirty power exports. Another cluster with similar
dynamics is found in southeastern Europe between the countries Greece, Bosnia-
Herzegovina, Albania, Montenegro, and Serbia. The correlation pattern here is,
however, not easily interpreted.

Figure 5: Utilization of national emission targets - a) A box plot of the
utilization of the national reduction targets for the individual countries
across all scenarios. A value of 100% means that the country is emitting as
much CO2 as their reduction target allows, whereas 0% indicates that the
country has no emissions although the CO2 reduction target is not 0. The
reduction configurations Efficiency 55% and Efficiency 70% are not included on
the figure as they per definition utilize all assigned emissions. b) Example
countries. Reduction target utilization plotted against the total amount of
target emissions.

In this study, CO2 reduction targets were assigned to countries giving the
countries the option to either use all allowable emissions or simply leave
them unused if it is economically optimal. The top panel of Figure 5 shows a
box plot of the utilization of the national reduction targets for the
individual countries across all configurations of national reduction target
allocations. Here, a value of 100% means that the country is emitting as much
CO2 as their reduction target allows, whereas 0% indicates that the country
has no emissions although the CO2 reduction target is not 0. Below the box
plot, the probability of full reduction target utilization has been shown for
five illustrative countries (Figure 5). It features three distinct behavioral
patterns for the countries. The countries either a) emit as much as the
national target allows no matter what, b) sometimes overperform on the target
or c) never have any emission. These different patterns are clearly
highlighted in the lower panels: Poland is seen always emitting as much as the
national target allows. The Netherlands, Austria, and Finland can be seen to
be frequently over-performing, with less than the allowable emissions. The
curved lines appearing in these figures correspond to the countries capping
out at a certain emission level. Finland can be seen having a clear upper
bound to how much CO2 they will choose to emit, whereas Austria appears to
have a wide range of possible outcomes available within the criteria used.
This behavior is very likely a result of the strong correlation between
Austria’s emissions with the emission from Germany and France found in Figure
4. In configurations where Germany is using less than their assigned
emissions, Austria is providing dispatchable power and therefore itself has
higher emissions. In scenarios where Germany and its neighbors have high
allowable emissions, the demand for dispatchable power imports from Austria
drops, and it becomes cost-optimal for Austria not to use all the assigned
emissions.

Studying how the five CO2 allocation approaches from Table 2 are distributed
on Figure 5 reveals that the Efficiency approach ensures that all national
emission quotas are utilized 100%. In the Efficiency scheme, no country is
assigned more emissions than needed, whereas the other allocation approaches
result in inefficient allocations increasing total system cost. Especially the
Grandfathering scheme leads to a large share of assigned emissions being left
unused. It should be noted, that as only the electricity sector is considered
in this research, the 55% reduction target provides a somewhat conservative
benchmark, considering that the electricity sector is expected to be the first
to be decarbonized. As several countries already have decarbonized their
electricity sector to a high extent, they can be expected to find it
economically optimal to avoid using all the emissions they are assigned.
Norway, Sweden, and Switzerland can be seen to refrain from using their
allocated emissions in most configurations of national reduction target
allocations. This is in accordance with the findings shown in Figure 3.

Figure 6: National CO2 abatement costs and electricity prices - a) National
CO2 abatement costs for all countries across all scenarios. The countries are
sorted after average emission per Mwh produced. b) Annualy averaged hourly
electricity price for the individual countries across all scenarios.

Imposing a limit on national CO2 emissions naturally triggers a shadow price
on emissions abatement. In a linear optimization model such as the one used in
this paper, the Lagrange/Karush Kuhn-Tucker multiplier of the national CO2
constraints serves as a proxy for the national CO2 abatement cost. The
Lagrange multiplier measures the change in objective function value caused by
a marginal change in the given constraint. Thus, the Lagrange multiplier
associated with the national emission limits measures the increase in total
system costs, when the given node is constrained on its emissions. CO2
abatement costs for all modeled configurations and approaches are shown in the
top panel of Figure 6. Equivalently, the hourly national electricity price can
be found as the Lagrange multiplier value of the national electricity balance
constraints. Average electricity prices are shown on the lower panel of Figure
6. For the formulation of the linear optimization problem, including the
national CO2 constraint, and the nodal energy balance constraints, refer to
the Appendix.

CO2 abatement costs are highly dependent on national CO2 reduction targets and
the availability of renewable or low-carbon resources. A marginal abatement
cost will only occur if the national emission reduction constraint is binding.
Thus, in a scenario where a given country is only utilizing parts of the
allocated CO2 quota, an abatement cost of 0 will be obtained. In Figure 5 it
is seen that a large number of the model countries are not utilizing the
entire share of allocated emissions. Therefore, CO2 abatement costs of zero
are seen for several countries in many of the outcomes in Figure 6.
Considering the group of countries, which always utilize their allocated
emissions (see Figure 5), and their incurred CO2 abatement costs shown in
Figure 6, these countries are seen to always have non-zero abatement costs.
The abatement costs for these countries are ranging from 30 to 40 € per ton
CO2 in most configurations of national reduction target allocations, but with
outliers ranging much higher.

On the top panel of Figure 6, the Efficiency schemes are seen having a uniform
global CO2 abatement cost determined by the joint emissions reduction target.
The change in global CO2 abatement costs between the Efficiency
configurations, with 55% and 70% reduction are reflecting the increased socio-
economic burden associated with higher emissions reductions.

Electricity prices are found to have a smaller spread for the individual
countries as seen on the lower panel of Figure 6. The robustness of the
electricity price does, however, depend on the country observed with countries
at each end of the figure having more robust prices, and countries towards the
center having larger deviations. The countries observed to have constantly
high prices are to a large extent the same countries that had high abatement
costs. The cluster of countries observed to have high fluctuations in the
electricity price is also the countries observed having strong correlations in
national CO2 emissions on Figure 4. The observed electricity prices on the
lower panel of Figure 6 span from 10 €/MWh to above 70 €/MWh for some outlier
outcomes. This span in power prices is rather large compared to current power
prices which are around 50 €/MWh for most European countries.

##  4 Discusion

What has been considered here are possible reduction target configurations (or
should we say obligations?) for the European power sector to reach a joint
decarbonization target of 55% (base-year 1990). This is not to be confused
with strict quota allocation schemes, as the perspective here is broader and
includes other more equitable allocation principles.

The power sector is currently subject to ETS; this article has considered
possible other options highlighting four equity-based allocating
configurations. Outcomes are in all cases challenging to predict due to the
interlinked nature of electricity markets, however, an attempt was included to
take account of transnational power interconnections and their capacities.

A fully efficient outcome is hard to obtain, as it requires close coordination
and full information. Although in theory, EU ETS should ensure an efficient
outcome, in practice information asymmetries are distorting the clearing of
markets. Moreover, there are sunk costs causing dirty power producers to
continue operating, due to the differences between marginal and average costs
of production.

EU ETS is not equitable. The price of emission permits is the same across
Europe, despite differences in GDP, income, and purchasing power. Countries
with low incomes tend to have inefficient and dirty power sectors, further
reinforcing the inequities, as the costs to shoulder with decarbonization tend
to be relatively larger to them. The commission proposes to create an ETS2 for
transport and households, hence relevant to explore alternative allocation
principles and their implications. Especially so as the Just Transition Fund
is relatively loosely described.

The comprehensive modeling shows that although a wide range of outcomes is
possible, most configurations will, despite differences in allocation
principles, result in rather high electricity prices in all the ‘new’ member
states in CEE, while the ’old’ benefit from lower prices, especially so the
Nordic countries, UK, and Spain.

The differences in abatement costs per unit of carbon can be misleading as to
the distributional consequences, as the abatement effort will be less
demanding in countries that are already partly decarbonized such as France.
Still, not only can unit costs be expected to be relatively high in Balkan
countries, but these countries are also facing a greater transformation
overall, involving high absolute costs.

An overlap can be observed between the group of countries experiencing high
abatement costs and the countries experiencing high electricity prices
(Slovakia, Greece, Poland, Macedonia, Bulgaria, Romania). Countries included
in both groups include several Eastern European and Balkan countries. As these
countries also have a tendency to have high income inequality, increasing
electricity prices may significantly grow energy poverty.

The allocation principle of sovereignty results in the highest cost overshoot,
showing the value of European cooperation. Still, the fluidity of the
transactions in the power market and the facilitation of more interconnectors
are making planning for decarbonization challenging. Some countries in the
center of Europe are facing many different feasible outcomes, whereas
countries in the periphery (Finland) will have fewer choices to make. The
vision of a fully interconnected Europe is still only a distant dream.

The modeling shows that CO2 intensity will, despite fulfillment of the 55%
target, remain high in Poland and other eastern countries, and continue to do
so at a 70% reduction under the EU ETS. Thus, providing a trail of high carbon
costs well into the future under the EU ETS. Following the sovereignty
configurations principle would result in a more equitable distribution of CO2
intensity, but it will drive higher CO2 abatement costs in Poland and other
countries with high emission intensities. Overall the difference between the
egalitarianism and ability-to-pay configuration principle is limited – the
former may provide proxies that are easier to implement.

##  5 Conclusion

EU ETS ensures efficient decarbonization of the European electricity sector
but fails to provide a just energy transition. This paper investigates
possible alternatives to EU ETS capable of delivering higher equity at minor
cost increases. By performing a global sensitivity analysis on national
emission reduction targets using an MCMC method, in combination with an energy
system optimization model, approximate distributions of all possible reduction
target configurations are revealed.

The range of possible national CO2 reduction targets identified for the
European electricity supply reveals that a cost increase of 5% from the cost-
optimal solution is almost inevitable. Small deviations from the cost-optimal
configuration of national CO2 reduction targets will lead to increases in
total system cost. Accepting a moderate increase in system cost reveals a
large range of possible alternatives to the configuration of national
reduction targets obtained under EU ETS. Although some flexibility is
available, countries, where emissions are hard to reduce, are found to have a
high CO2 emission intensity in the majority of configurations. A strong
correlation between emissions within three groups of countries located in
central, North Eastern, and South-Eastern Europe were identified. These
correlations reveal that enforcing a tight CO2 limit on one cluster country
will move emissions to the other countries in the cluster. The likely
explanation for this behavior is that carbon leakage between neighboring
countries will occur when differences in national CO2 abatement cost increase.
Analyzing the utilization of allocated emissions reveals a group of countries
where it will be economically favorable to decarbonize the power sector, thus,
having zero emissions even when emissions are allocated to the given country.
A large group of countries does, however, favor some level of emissions from
the power sector, but the level of favored emissions does, in many cases,
depending on emissions from neighboring countries. National CO2 abatement cost
associated with the sampled emission allocation schemes reveals large
inequality with some countries being likely to have significantly higher
abatement costs. A similar picture is found when studying power prices. The
key takeaway from this study is the fact that the burden of transitioning our
power supply is inequitably distributed, and actions must be taken to
compensate.

##  6 Acknowledgments

Financial support (grant #82841) from Nordforsk, Nordic Energy and Nordic
Innovation to the project NOWAGG (New Nordic Ways to Green Growth;
https://projects.au.dk/nowagg/). Tim T. Pedersen, M. Victoria nad Gorm B.
Andresen are fully or partially funded by the RE-INVEST project, which is
supported by the Innovation Fund Denmark under grant number 6154-00022B. Tim
T. Pedersen and Gorm B. Andresen are partialy fundet by DFF-Dansk ERC-
støtteprogram (case number: 1105-00001B).

Assistance and input given by Martin Greiner was greatly appreciated.

##  7 Author contributions

Conceptualization T.T.P, M.V. and G.B.A; Methodology T.T.P; Software T.T.P;
Resources M.V.P and G.B.A; Writing - Original Draft T.T.P. and M.S.A; Writing
- Review & Editing T.T.P, M.S.A, M.V, and G.B.A; Funding Acquisition G.B.A;

##  8 Declaration of competing interest

The authors declare no competing interests.

##  Appendix A Resource availability

#### Lead contact

Tim Pedersen, Email<EMAIL_ADDRESS>
#### Description

The developed python scripts used in the paper are available under an open-
source license. All scripts and data required to reproduce the results from
this paper are openly available.

#### License

The software is under the GNUv3 license

#### Data and code availability

Link to repository doce will be public upon completion of review

##  Appendix B Sampling method

To draw possible CO2 target configurations the Adaptive Metropolis-Hastings
(AMH) sampler is implemented [21]. The AMH sampler is based around a Markov
Chain process where samples are continuously drawn from a proposal
distribution centered around the previous sample point. By controlling the
width of the proposal distribution continuously, the AMH sampler ensures
efficient sampling. The AMH sampler is chosen as it is simple to implement
while providing efficient sampling and fast mixing [28].

Figure 7: Sampling method schematic

An arbitrary CO2 target configurations can be denoted as the vector
$\mathbf{x}$, with each component of this vector $x_{i}$ representing the
national CO2 emission target of the $i$’th country relative to the total CO2
emission target. The allowed emission for a given country can be determined as
$x_{i}\cdot CO2_{CAP}$, where the $CO2_{CAP}$ is the total global amount of
CO2 emissions allowed in tonnes of CO2. Realizations of the variables are
denoted with subscript $\mathbf{x}_{t}$. It is important to note that the sum
of $\mathbf{x}$ can be greater than 1, and thus the combined emission targets
can add up to more than the total global amount of CO2 emissions allowed
$CO2_{CAP}$. As the rejection criteria is based on the realized emissions, a
sample where the sum of $\mathbf{x}$ is greater than 1 can be accepted if not
all allowed emissions are realized. Similarly $\mathbf{x}$ can also sum to
less than 1. In such a case the global emission reductions will be less than
the required 55% and the sample can be immediately rejected.

Given a starting point $\mathbf{x}_{0}$ the AMH sampler will continuously
generate new sample proposals $\mathbf{x}^{\prime}$. New samples are drawn
from the proposal distribution centered around the previous sample. The
proposal distribution is defined as a uniform distribution around the previous
sample point with the width $\sigma$. Thus the maximal change in each variable
$x_{i}$ per iteration is $\sigma/2$. There are however a few caveats. As the
variables considered $\mathbf{x}$ are fractions of a total CO2 budget, they
are constrained to be between 0 and 1. Therefore, the uniform distribution is
bounded not to exceed this area. The starting point $\mathbf{x}_{0}$ used is
the cost-optimal scenario also denoted as the Efficiency scenario. A burn-in
period of 100 samples is used by discarding the first 100 samples of each
chain to remove any bias towards the starting point.

$\mathbf{x}^{\prime}\sim\mathcal{U}[\max(\mathbf{x}_{t-1}-\frac{\sigma}{2},0),\min(\mathbf{x}_{t-1}+\frac{\sigma}{2},1)]$
(1)

The distribution width $\sigma$ is tuned continuously as more information
about the solutions space is obtained. By setting $\sigma$ too low, the
sampler will need an excessive amount of samples to explore the entire
solution space. On the other hand, setting $\sigma$ too high will result in
the rejection of too many samples. By continuously monitoring the acceptance
rate, it is possible to determine if the chain is taking either too short or
long steps. If the acceptance rate is very high $\sigma$ should be increased,
and if the acceptance rate is low $\sigma$ should be decreased. In practice,
this is implemented by letting the sampler run for a number of iterations and
evaluating the acceptance rate in that batch of samples. In this
implementation of the AMH sampler, $\sigma$ is updated by continuously
monitoring the acceptance ratio of the samples. When the acceptance ratio is
below a user-specified value, $\sigma$ is incremented by a small amount
$\epsilon$, and vice versa when the acceptance ratio is too high. An
$\epsilon$ value of 0.05 and a desired acceptance ratio of 80% have been used
throughout this work.

The feasibility of a proposed sample $\mathbf{x}^{\prime}$ is evaluated using
the energy system optimization model. If the solution to the energy system
optimization model given $\mathbf{x}^{\prime}$ as input satisfies all criteria
from Table 1, the sample is accepted. Otherwise, the sample is rejected and a
new proposal sample is drawn. When a proposed sample is accepted it is
assigned index $t$, such that $\mathbf{x}_{t}=\mathbf{x}^{\prime}$. If a
sample is rejected the previous sample point is stored instead
$\mathbf{x}_{t}=\mathbf{x}_{t-1}$. The process of drawing samples from the
proposal distribution and either accepting or rejecting them is repeated until
sufficient sample size is reached. The process is illustrated in Figure 7.

The result is a set of realizations of $\mathbf{x}$ that can ensure feasible
operation of the model, global emission reductions higher than the base
scenario, and a total system cost that is no more than 18% higher than that of
the base scenario. If enough samples are drawn the distribution of the set of
realizations will approximate all solutions satisfying the above-mentioned
criteria.

In practice, the above algorithm is implemented as a parallel process with
multiple chains running simultaneously. The samples from the parallel chains
can then be merged at the end of the sampling process.

##  Appendix C Energy system optimization model

The joint capacity and dispatch optimization model used in this work is based
on the PyPSA-Eur-Sec model [26]. The PyPSA-Eur-Sec model to a high extend
depends on data imports from the PyPSA-Eur model [29]. The model formulated in
this work represents a 2030 brownfield scenario of the European electricity
supply spanning 33 ENTSO-E member countries. All existing plus the planned
transmission capacities in the Ten Year Network Development Plan (TYNDP) [27]
is included. Transmission capacities are seen in Figure 1.

A brownfield scenario is generated where existing capacities that are planned
to be in operation by 2030 are included in the model. The included brownfield
capacities are seen in Table 5. Existing conventional capacities are found
from the power plant matching database [30], while renewable capacities are
found from the IRENA annual statistics [31]. A minimum requirement of 55% CO2
reductions have been used throughout this work, corresponding to an annual CO2
budget of 666.85 Mton CO2.

Some technology capacities can be expanded to meet energy demand at a certain
cost. Cost of the expandable technologies are given in Table 3. Efficiency and
emission data are available in Table 4. Technology costs are primarily based
on the 2030 cost prediction given by the Danish Energy Agency in their
technology data catalog [32]. A discount rate of 7% has been used to calculate
annualized costs using the annuity factor given in Equation 2. Here $r$ is the
discount rate and $n$ is the technology lifetime.

$a=\frac{1-(1+r)^{-n}}{r}$ (2)

The model of the European power sector is formulated as a linear optimization
problem, consisting of an objective function along with a set of constraints.
Throughout this description of the model, the model variables are split in two
vectors namely $\mathbf{x}$ and $\mathbf{y}$. Where $\mathbf{x}$ describes the
national CO2 reduction target given by the MCMC sampler
$\mathbf{x}={r_{n}\;\forall\;n}$. Here $r_{n}$ is the national CO2 target in
tons CO2 for all model countries $n$. The remaining variables $\mathbf{y}$
represent technology capacities and dispatch
$\mathbf{y}=\\{\mathbf{g}_{n,s,t},\mathbf{G}_{n,s},\mathbf{F}_{l}\\}$. Here
index $s$ is indexing the technology for all technologies included in the
model, index $t$ is indexing the hour for all hours in the year, and $l$
represent the transmission line. The variables determined in the optimization
process are thus:

  * 1.

$\mathbf{g}_{n,s,t}$ : Hourly dispatch of energy from the given plants in the
given countries with the marginal cost $\mathbf{o}_{n,s}$.

  * 2.

$\mathbf{G}_{n,s}$: Total installed capacity of the given technologies in the
given countries with the capital cost $\mathbf{c}_{n,s}$.

  * 3.

$\mathbf{F}_{l}$: Total installed transmission capacity for all lines with the
fixed annualized capacity cost $\mathbf{c}_{l}$.

The model is then formulated as a linear problem following the standard
formulation given as:

$\begin{split}\text{minimize}\;&\;\mathbf{f}_{0}(\mathbf{y})\;\\\
\text{subject to}\;&\;\mathbf{f}_{i}(\mathbf{x,y})\leq 0\;\;i=1..m\\\
\;&\;\mathbf{h}_{i}(\mathbf{x,y})=0\;\;i=1..p\\\ \end{split}$ (3)

The national CO2 targets $\mathbf{x}$ are given by the MCMC sampler and are
thus not optimized in the model. Only the technical variables $\mathbf{y}$ are
optimized in the optimization problem.

The objective function of the model is to minimize total system cost and can
be formulated as follows:

$\text{minimize}\;f_{0}(\mathbf{x,y})=\sum_{n,s}\mathbf{c}_{n,s}\mathbf{G}_{n,s}+\sum_{l}\mathbf{c}_{l}\mathbf{F}_{l}+\sum_{n,s,t}\mathbf{o}_{n,s}\mathbf{g}_{n,s,t}$
(4)

The model assumes perfect competition and foresight as well as long-term
market equilibrium. For all model nodes and all hours in the year, a power
balance constraint is enforced requiring that the energy demand
$\mathbf{d}_{n,t}$ is fulfilled. Energy demand data is taken from the ENTSO-E
data portal [33] and decomposed in industrial and residential demand following
the method given in [29]. The incidence matrix describing the line connections
is given by $\mathbf{K}_{n,l}$ and the hourly power flowing through each line
is described as $\mathbf{f}_{l,t}$. The nodal power balance constraint can
then be formulated as:

$\sum_{s}\mathbf{g}_{n,s,t}-\mathbf{d}_{n,t}-\sum_{l}\mathbf{K}_{n,l}\mathbf{f}_{l,t}=0\;\;\forall
n,t$ (5)

The dispatch of each technology $\mathbf{g}_{n,s,t}$ is limited by the
installed technology capacity $\mathbf{G}_{n,s}$. The dispatch of renewable
energy generators such as wind and solar are furthermore limited by the hourly
capacity factor $\mathbf{\overline{g}}_{n,s,t}$. The capacity factor for
conventional power plants is 1, whereas it is generated from weather data for
the renewable generators. A detailed explanation of the derivation of
renewable generation potentials is given in [29].

$0\leq\mathbf{g}_{n,s,t}\leq\mathbf{\overline{g}}_{n,s,t}\mathbf{G}_{n,s}\;\forall
n,s,t$ (6)

Similarly, the power $\mathbf{f}_{l,t}$ flowing through the transmission lines
is also limited by the installed capacity. As the direction of the
transmission is without significance it is the absolute transmission
$|\mathbf{f}_{l,t}|$ that is limited.

$|\mathbf{f}_{l,t}|\leq\mathbf{F}_{l}\;\forall l,t$ (7)

The maximum capacity allowed for each technology is determined by geographical
potentials available $\mathbf{G}_{n,s}^{max}$.

$0\leq\mathbf{G}_{n,s}\leq\mathbf{G}_{n,s}^{max}\;\forall n,s$ (8)

CO2 emissions can be constrained in two ways. Either through a global
constraint on emissions, or by national constraints on emissions. The global
CO2 reduction constraint is formulated as:

$\sum_{n,s,t}\frac{1}{\mathbf{\eta}_{s}}\mathbf{g}_{n,s,t}\mathbf{e}_{s}-CAP_{CO_{2}}\leq
0\;$ (9)

Here the $CAP_{CO_{2}}$ is the global emissions limit given in ton CO2.
$\mathbf{\eta}_{s}$ is the generator efficiency and $\mathbf{e}_{s}$ is the
CO2 equivalent emission intensity of the fuel. Note that only a single
constraint is given here. Limiting emissions through national constraints can
be done by defining a constraint for each country in the model. The national
emissions targets $\mathbf{x}$ are given by the MCMC sampler.

$\sum_{s,t}\frac{1}{\mathbf{\eta}_{s}}\mathbf{g}_{n,s,t}\mathbf{e}_{s}-\mathbf{r}_{i}\leq
0\;$ (10)

The global CO2 constraint (Equation 9) is only used in the Efficiency
scenario. In all other scenarios, the national CO2 targets are explicitly
given, either by the sampler or following a certain allocation scheme.

When the model is solved the Lagrange multipliers associated with every
constraint are also obtained as an output. The value of these Lagrange
multipliers represents the cost increase/decrease associated with
tightening/loosening the constraint by one unit. Thus by evaluating the
Lagrange multipliers associated with the energy balance constraint (Equation
5) the nodal hourly electricity price can be obtained. Similarly, the Lagrange
multiplier of the national CO2 target constraint (Equation 10) provides a
proxy for the national CO2 abatement cost.

Table 3: Technology costs of new technologies. Technology | Capital cost | FOM | VOM | Lifetime
---|---|---|---|---
| Eur/kW | %/year | Eur/MWh | years
OCGT | 435.2 | 1.78 | 4.5 | 25
Offshore wind turbine | 1573.2 | 2.29 | 2.67 | 30
Offshore wind AC connection submarine | 2685.0* | 0 | 0 | 30
Offshore wind AC connection underground | 1342.0* | 0 | 0 | 30
Offshore wind AC station | 250.0 | 0 | 0 | 30
Offshore wind DC connection submarine | 2000.0* | 0 | 0 | 30
Offshore wind DC connection underground | 1000.0* | 0 | 0 | 30
Offshore wind DC station | 400 | 0 | 0 | 30
Onshore wind | 1035.6 | 1.22 | 1.35 | 30
Utility scale solar PV | 376.3 | 1.93 | 0 | 40
Electrolysis | 550.0 | 5.0 | 0 | 25
Fuel Cell | 1100.0 | 5.0 | 0 | 10
Hydrogen storage tank | 44.0** | 1.11 | 0 | 30
Hydrogen underground storage | 2.0** | 0 | 0 | 100
Battery inverter | 160.0 | 0.34 | 0 | 25
Battery storage | 142.0** | 0 | 0 | 25
* Eur/MW/km |  |  |  |
* Eur/kWh |  |  |  |
Table 4: Technology data. Emissions are given as t CO2 per MWh electricity produced. Technology |  Efficiency |  Emissions
---|---|---
|  % |  ton CO2/MWhe
OCGT |  41 |  0.49
CCGT |  58 |  0.34
Coal plant |  33 |  1.00
Lignite plant |  33 |  1.24
Oil plant |  35 |  0.77
Electrolysis |  66 |  0
Fuel Cell |  50 |  0
Battery inverter |  96 |  0
Table 5: Existing generator technology capacities by 2030 in MW |  Offshore wind |  Onshore wind |  Run off river |  Solar PV |  CCGT |  OCGT |  Coal |  Lignite |  Nuclear |  Oil
---|---|---|---|---|---|---|---|---|---|---
AT |  0.0 |  3132.7 |  4478.5 |  1438.6 |  2481.7 |  1313.5 |  991.5 |  0.0 |  0.0 |  0.0
BA |  0.0 |  50.6 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0
BE |  1185.9 |  2074.8 |  59.0 |  3984.5 |  3801.9 |  1460.6 |  1524.8 |  0.0 |  5925.8 |  0.0
BG |  0.0 |  691.0 |  22.4 |  1029.0 |  0.0 |  782.0 |  4963.7 |  3993.0 |  2000.0 |  0.0
CH |  0.0 |  63.0 |  5280.0 |  2171.0 |  0.0 |  0.0 |  0.0 |  0.0 |  3430.0 |  0.0
CZ |  0.0 |  316.2 |  40.2 |  2074.3 |  336.8 |  0.0 |  7184.7 |  725.7 |  2660.0 |  0.0
DE |  6396.0 |  52447.0 |  2997.0 |  45179.0 |  18120.9 |  8044.3 |  28069.4 |  20833.5 |  15788.4 |  3696.4
DK |  1708.1 |  4431.2 |  0.0 |  991.0 |  100.0 |  1427.4 |  3629.9 |  0.0 |  0.0 |  665.0
EE |  0.0 |  329.8 |  0.0 |  25.4 |  173.0 |  250.0 |  0.0 |  0.0 |  0.0 |  2111.0
ES |  0.0 |  23433.1 |  16.4 |  4753.5 |  24344.3 |  2942.6 |  6519.7 |  3081.2 |  7572.6 |  3533.4
FI |  67.0 |  1971.3 |  1289.6 |  123.0 |  648.0 |  677.7 |  3039.7 |  0.0 |  2784.0 |  1225.4
FR |  0.0 |  14898.1 |  5780.8 |  9604.0 |  5611.0 |  1066.0 |  4293.3 |  0.0 |  63130.0 |  7172.1
GB |  8212.7 |  13553.9 |  685.2 |  13107.3 |  32824.3 |  921.5 |  14475.0 |  0.0 |  11261.0 |  2801.9
GR |  0.0 |  2877.5 |  103.1 |  2650.6 |  4482.0 |  417.0 |  1550.0 |  3905.0 |  0.0 |  0.0
HR |  0.0 |  580.3 |  278.7 |  67.4 |  369.6 |  82.5 |  304.3 |  0.0 |  0.0 |  647.8
HU |  0.0 |  335.0 |  19.7 |  724.0 |  1259.2 |  2368.7 |  42.3 |  1180.2 |  1886.8 |  410.0
IE |  25.2 |  3650.9 |  216.0 |  21.8 |  2946.0 |  1320.0 |  855.0 |  0.0 |  0.0 |  907.0
IT |  0.0 |  10230.2 |  6563.7 |  20073.6 |  34438.1 |  6491.8 |  10926.5 |  0.0 |  0.0 |  6145.0
LT |  0.0 |  532.0 |  0.0 |  81.9 |  0.0 |  1575.0 |  0.0 |  0.0 |  0.0 |  0.0
LU |  0.0 |  114.2 |  30.9 |  124.7 |  350.5 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0
LV |  0.0 |  62.9 |  642.1 |  0.0 |  1025.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0
ME |  0.0 |  118.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0
MK |  0.0 |  37.0 |  41.6 |  17.0 |  0.0 |  0.0 |  0.0 |  824.0 |  0.0 |  0.0
NL |  957.0 |  3491.0 |  0.0 |  4522.0 |  13582.0 |  3991.0 |  5591.0 |  0.0 |  492.0 |  0.0
NO |  0.0 |  1708.0 |  0.0 |  53.4 |  450.0 |  773.1 |  0.0 |  0.0 |  0.0 |  0.0
PL |  0.0 |  5762.1 |  14.4 |  562.0 |  326.0 |  1032.9 |  21588.5 |  9406.0 |  0.0 |  345.0
PT |  0.0 |  5172.4 |  1615.5 |  665.4 |  3829.0 |  0.0 |  1756.0 |  0.0 |  0.0 |  0.0
RO |  0.0 |  3243.0 |  870.4 |  1385.7 |  1080.0 |  2282.0 |  1506.0 |  4779.2 |  1298.0 |  87.5
RS |  0.0 |  25.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0
SE |  204.0 |  7097.0 |  1955.9 |  481.0 |  708.0 |  0.0 |  130.0 |  0.0 |  9532.0 |  2135.0
SI |  0.0 |  0.0 |  861.3 |  251.8 |  832.0 |  449.0 |  246.0 |  944.0 |  727.0 |  143.6
SK |  0.0 |  0.0 |  641.3 |  533.0 |  648.0 |  0.0 |  440.0 |  486.0 |  1940.0 |  0.0
Figure 8: CO2 target layouts for the scenarios used and the 150% coal
production upper limit. The 150% coal upper limit is calculated as the load of
each nation multiplied by an emission factor of 0.45[tCO2 per MWh] times 1.5.

##  Appendix D Scenarios with equal realized emissions

In this work, a decision was made to compare scenarios (see Table 2) that
assign CO2 targets summing up to the same total CO2 budget. The CO2 targets
are not always fully utilised as some countries find it economically favorable
to reduce emissions despite being assigned allowable emissions. The result is
that the scenarios compared have different global emission reductions although
having the same CO2 budget as seen in Figure 2. The shares of unused CO2
emissions is seen in Figure 5. Alternatively, one could design the scenarios
to have equal realized global emissions. By adjusting the CO2 budget for the
individual scenarios, realized emissions corresponding to a 55% emission
reduction can be achieved. Figure 9 b) shows the relationship between assigned
emissions and realized emissions for all configuration strategies listed in
Table 2. The figure clearly shows configuration strategies other than
Efficiency having lower realized than assigned emissions. Figure 9 a) shows
the cost increase associated with the unused CO2 emissions. A cost increase
for the configuration strategies is seen even when the realized emissions
correspond to a 55% CO2 reduction for all strategies.

Figure 9: a) Shows the relationship between cost increase and CO2 reduction
for all configuration strategies. b) Realized CO2 emissions from all
configuration strategies plotted against the sum of assigned CO2 targets. The
horizontal black line represents the CO2 budget associated with a 55% CO2
reduction.

In this section the result found by selecting scenarios with realized
emissions corresponding to a 55% CO2 reduction is shown. Figure 11 shows
figures corresponding to Figure 3 and 6, but the configuration strategies
shown all have realized emissions corresponding to a 55% CO2 reduction. Thus
the configurations shown here all have higher realized emissions then the
configurations used in Figure 3 and 6. The configurations studied in this
section with realized emissions corresponding to a 55% CO2 reduction will be
referred to as the ”55% realized” configurations, whereas the original
scenarios with equal CO2 budgets will be referred to as the ”55% CO2 budget”
configurations.

Comparing the ”55% CO2 budget” configurations found on Figures 3 and 6 with
the ”55% realized” configurations, found on Figure 11, the ”55% realized”
configurations are found to be more equal. Across all measures shown in Figure
11, the ”55% realized” configurations deviate less from each other than the
”55% CO2 budget” configurations does on Figures 3 and 6. This behavior is
expected as the ”55% realized” configurations redistribute unused CO2 from
countries finding it favorable to reduce emissions, to countries where higher
emissions are desired. Thus, the ”55% realized” configurations become more
similar to the Efficiency configuration compared to the ”55% CO2 budget”
configurations. This is also reflected in the significant cost decrease
between the ”55% realized” and ”55% CO2 budget” configuration shown on Figure
9 a). Furthermore, Figure 10 shows how the ”55% realized” scenarios have much
less unused CO2 emissions than the ”55% CO2 budget” configuration.

Figure 10: Unused emissions given as the fraction of the national target used,
for scenarios that all have realized emissions corresponding to a 55% CO2
reduction.

Figure 11: The three figures shows results for scenarios that all have
realized emissions corresponding to a 55% CO2 reduction. Panel a) shows
relative emissions on country level. Panel b) shows abatement cost, and panel
c) shows electricity prices.

## References

  * [1] Secretariat-General, Communication from the commission - the european green deal, Tech. rep., European Council (2019).
URL https://eur-lex.europa.eu/legal-content/EN/ALL/?uri=COM:2019:640:FIN

  * [2] K. Jenkins, D. McCauley, R. Heffron, H. Stephan, R. Rehner, Energy justice: a conceptual review, Energy Research & Social Science 11 (2016) 174–182.  doi:https://doi.org/10.1016/j.erss.2015.10.004.
  * [3] D. Maguire, C. Shaw, Fair energy transition for all - literature review, Tech. rep., Climate Outreach (2021).
  * [4] Eu emissions trading system (eu ets), Tech. rep., European Council (2021).
URL https://ec.europa.eu/clima/policies/ets_en

  * [5] The just transition mechanism, Tech. rep., European Council (2021).
URL https://ec.europa.eu/info/strategy/priorities-2019-2024/european-green-
deal/finance-and-green-deal/just-transition-mechanism_en

  * [6] 2030 climate and energy framework, Tech. rep., European Council (2021).
URL https://ec.europa.eu/clima/policies/strategies/2030_en

  * [7] 2030 climate target plan, Tech. rep., Council of European Union (2021).
URL https://ec.europa.eu/clima/policies/eu-climate-action/2030_ctp_en

  * [8] Regulation (eu) 2018/842 of the european parliament and of the council of 30 may 2018 on binding annual greenhouse gas emission reductions by member states from 2021 to 2030 contributing to climate action to meet commitments under the paris agreement and amending regulation (eu), no 525/2013, Tech. rep., Council of European Union (2018).
URL http://data.europa.eu/eli/reg/2018/842/oj

  * [9] M. Schlott, O. E. Sayed, M. Bilousova, F. Hofmann, A. Kies, H. Stöcker, Carbon leakage in a european power system with inhomogeneous carbon prices, arXivdoi:https://arxiv.org/abs/2105.05669.
  * [10] W. Nordhaus, Climate change: The ultimate challenge for economics, American Economic Review 109 (6) (2019) 1991–2014.  doi:DOI:10.1257/aer.109.6.1991.
  * [11] M. Victoria, K. Zhu, T. Brown, G. B. Andresen, M. Greiner, Early decarbonisation of the european energy system pays off, Nature communications 11 (1) (2020) 1–9.  doi:https://doi.org/10.1038/s41467-020-20015-4.
  * [12] Eurostat, Greenhouse gas emissions by source sector, Tech. rep., Eurostat (2019).
URL https://ec.europa.eu/eurostat/web/products-datasets/-/sdg_13_10

  * [13] A. Levenda, I. Behrsin, F. Disano, Renewable energy for whom? a global systematic review of the environmental justice implications of renewable energy technologies, Energy Research & Social Science 71 (2021) 101837.  doi:https://doi.org/10.1016/j.erss.2020.101837.
  * [14] O. Golubchikov, K. O’Sullivan, Energy periphery: Uneven development and the precarious geographies of low-carbon transition, Energy and Buildings 211 (2020) 109818.  doi:https://doi.org/10.1016/j.enbuild.2020.109818.
  * [15] P. Zhou, M. Wang, Carbon dioxide emissions allocation: A review, Ecological Economics 125 (2016) 47–59.  doi:10.1016/j.ecolecon.2016.03.001.
  * [16] O. Alcaraz, P. Buenestado, B. Escribano, B. Sureda, A. Turon, J. Xercavins, Distributing the global carbon budget with climate justice criteria, Climatic change 149 (2) (2018) 131–145.  doi:https://doi.org/10.1007/s10584-018-2224-0.
  * [17] B. K. Sovacool, M. H. Dworkin, Energy justice: Conceptual insights and practical applications, Applied Energy 142 (2015) 435–444.
  * [18] E. M. Markowitz, A. F. Shariff, Climate change and moral judgement, Nature Climate Change 2 (4) (2012) 243–247.  doi:https://doi.org/10.1038/nclimate1378.
  * [19] L. J. Schwenk-Nebbe, M. Victoria, G. B. Andresen, M. Greiner, Co2 quota attribution effects on the european electricity system comprised of self-centred actors, SSRN Electronic Journaldoi:https://doi.org/10.2139/ssrn.3689207.
  * [20] N. Bauer, C. Bertram, A. Schultes, D. Klein, G. Luderer, E. Kriegler, A. Popp, O. Edenhofer, Quantification of an efficiency–sovereignty trade-off in climate policy, Nature 588 (7837) (2020) 261–266.  doi:10.1038/s41586-020-2982-5.
  * [21] H. Haario, E. Saksman, J. Tamminen, et al., An adaptive metropolis algorithm, Bernoulli 7 (2) (2001) 223–242.  doi:https://doi.org/10.2307/3318737.
  * [22] E. D. Brill Jr, S.-Y. Chang, L. D. Hopkins, Modeling to generate alternatives: The hsj approach and an illustration using a problem in land use planning, Management Science 28 (3) (1982) 221–235.  doi:https://doi.org/10.1287/mnsc.28.3.221.
  * [23] F. Neumann, T. Brown, Broad ranges of investment configurations for renewable power systems, robust to cost uncertainty and near-optimality, arXivdoi:https://arxiv.org/abs/2111.14443.
  * [24] F. Lombardi, B. Pickering, E. Colombo, S. Pfenninger, Policy decision support for renewables deployment through spatially explicit practically optimal alternatives, Joule 4 (10) (2020) 2185–2207.  doi:https://doi.org/10.1016/j.joule.2020.08.002.
  * [25] F. Neumann, T. Brown, The near-optimal feasible space of a renewable power system model, Electric Power Systems Research 190.  doi:https://doi.org/10.1016/j.epsr.2020.106690.
  * [26] T. Brown, martavp, lisazeyen, M. Maria, Leon, F. Neumann, Pypsa/pypsa-eur-sec: Pypsa-eur-sec version 0.4.0 (2020).  doi:10.5281/zenodo.4317529.
  * [27] Ento-E, Ten year network development plan, Tech. rep., Ento-E (2018).
URL https://tyndp.entsoe.eu/tyndp2018/

  * [28] A. Solonen, P. Ollinaho, M. Laine, H. Haario, J. Tamminen, H. Järvinen, Efficient mcmc for climate model parameter estimation: Parallel adaptive chains and early rejection, Bayesian Analysis 7 (3) (2012) 715–736.  doi:https://doi.org/10.1214/12-BA724.
  * [29] J. Hörsch, F. Hofmann, D. Schlachtberger, T. Brown, Pypsa-eur: An open optimisation model of the european transmission system, Energy Strategy Reviews 22 (2018) 207–215.  doi:https://doi.org/10.1016/j.esr.2018.08.012.
  * [30] F. Hofmann, J. Hörsch, Fresna - powerplantmatching v.0.4.1 (2019).  doi:https://doi.org/10.5281/zenodo.3358985.
  * [31] Anual statistics, Tech. rep., IRENA (2019).
URL https://www.irena.org/Statistics/Download-Data

  * [32] Technology data catalogues, Tech. rep., Danish Energy Agency (2019).
URL https://ens.dk/en/our-services/projections-and-models/technology-data

  * [33] ENSTO-E, Data portal, "https://www.entsoe.eu/data/data-portal/consumption/" (2020).