# Enabling agency: trade-offs between regional and integrated energy systems
design flexibility

Koen van Greevenbroek111Contributed equally Corresponding author,
<EMAIL_ADDRESS>Department of Computer Science, UiT The Arctic
University of Norway, Postboks 6050 Langnes, 9037 Tromsø, Norway  Aleksander
Grochowicz11footnotemark: 1 Department of Mathematics, University of Oslo,
P.O. Box 1053 Blindern, 0316 Oslo, Norway  Marianne Zeyringer  Department of
Technology Systems, University of Oslo, P.O. Box 70, 2027 Kjeller, Norway
Fred Espen Benth  Department of Mathematics, University of Oslo, P.O. Box 1053
Blindern, 0316 Oslo, Norway

### Abstract

Europe as a whole as well as individual countries have many distinct pathways
to net carbon neutrality by 2050. We use novel near-optimal modelling
techniques to illuminate trade-offs and interactions between national and
continental energy transitions under uncertainty. Our results reveal extensive
and robust flexibility at a regional level in renewable and hydrogen
investments as well as in hydrogen and electricity exports. However, Europe’s
energy interconnections lead to significant cross-border effects of national
energy strategies. Wind and hydrogen investments can easily be shifted
geographically within Europe, and Northern Europe’s capacity as energy
exporter or importer can shape and be shaped by the remaining system. Solar in
Southern Europe and Germany comes out as an enabler, and can unlock design
flexibility for the rest of the system. Quantifying these regional trade-offs
in energy system planning is crucial in order to facilitate meaningful policy
discussion and enable a fair energy transition.

### Introduction

The European energy system is gearing up for a massive transformation towards
net carbon neutrality which will deeply change the production and flow of
energy both at the domestic and international level. Having enshrined
greenhouse gas neutrality by 2050 in the European Climate Law [1], the EU
plans to achieve the transition through a mix of the European Green Deal [12]
and national policy. Modelling studies have shown that there is flexibility in
regional and national investment choices; however this then impacts the
options for the rest of Europe [2, 36, 41, 32]. The regional dynamics of
decision making are thus identified as important for policy planning [20, 10,
39].

Energy system optimisation models play an important role in investigating how
to best reach European and national climate targets. Most such models,
however, optimise total system cost alone, thus inaccurately assuming a common
goal across the included countries [3]. While the spatial diversity of
potential carbon-neutral system designs has been explored [23, 34, 32, 36],
systematic studies delineating the design spaces of individual regions
embedded in a larger system are missing. Given the immense challenge of
decarbonising the European energy system by 2050, it is crucial to understand
the interactions of continental and national investment strategies including
imports, exports and mutual design flexibility — this prevents the design of
systems that are operationally inadequate, overdimensioned and/or socially
unjust.

To address this research gap, we use near-optimal methods with a sector-
coupled energy system optimisation model to conduct a rigorous study of the
effects of national policy on the future European energy system and vice
versa. Using a diverse set of scenarios to ensure robustness to uncertainty,
we obtain results for 7 key _focus regions_ embedded in the European energy
system. This enables a comparison of regional design flexibility, export
potentials and minimum investment levels subject to various system-wide policy
decisions.

Large varieties of system designs can be described by the near-optimal space
of an energy system model [8, 26, 33, 16]. The near-optimal space consists of
feasible model solutions that are marginally more expensive than the cost
optimum. Studying such solutions is important for policy advice since societal
or geopolitical considerations often take precedence over total system costs
[29, 24, 22]. Recent advances involve systematically mapping out
representations of near-optimal spaces [16, 33], facilitating better searches
for robust or otherwise desirable solutions. Common among these geometric
approaches is that they work with reduced near-optimal spaces, mapped down to
a small number of dimensions, for instance total investment by technologies
[26, 27].

Our innovation is to map out the near-optimal space in a set of dimensions
representing investment in key technologies both _inside_ and _outside_ a
given region. We concentrate on solar, onshore wind, offshore wind and
hydrogen infrastructure, resulting in a total of 8 dimensions. Approximations
of the resulting joint near-optimal design spaces [16] are then computed for
each of the 7 focus regions separately. Furthermore, we ensure robustness of
the results by intersecting near-optimal spaces [16] arising from scenarios
combining different technology costs, land use restrictions and weather years.
Our results primarily build upon the geometry of these intersections. The
intersection technique has previously only been applied to weather years; our
approach involving a variety of scenarios provides a novel blueprint for
future studies of robust system design.

We find a strikingly large degree of design flexibility — on the continental,
but even more so on the regional level. Investment in certain technologies and
regions affects system design flexibility much more than others, with for
example solar power in Germany being a system-wide enabler. Wind and hydrogen
investment, meanwhile, can be geographically shifted relatively freely,
revealing opportunities for individual regions to become renewable energy
exporters or hydrogen powerhouses. This significantly expands the results
pertaining to overall design flexibility within the renewable electricity
sector in Europe found in previous studies [16, 27, 34], precisely mapping the
considerable trade-offs between solar, onshore wind and offshore wind at a
regional resolution.

### Ample opportunities for regional energy supply and exports

On the system-wide continental level and especially on the regional level,
there is significant flexibility in investment in all explored technologies
(solar, on- and offshore wind, hydrogen). Even taking into account
uncertainties in costs, weather years and land use restrictions, we find a
large space of robust solutions, i.e. designs that are feasible under all
scenarios (Methods). Moreover, the connection to European energy markets
provides individual regions significantly more planning flexibility
(relatively speaking) than we see for the overall system. Allowing a small
cost increase beyond the cost-minimal design (here, 5%) gives room for
preferences and investment robustness that do not exist in the cost optimum.

We see that any robust European system design needs at least around 60 bn EUR
investment in onshore wind and solar power each, amounting to $\sim$500 GW and
$\sim$1250 GW of installed onshore wind and solar capacity, versus 188 GW [44]
and 209 GW [25] in EU-27 in 2022, respectively. Remaining investment can be
distributed in many different ways (Figure 1 (a)–(c)). Overall optimal system
costs in our different focus models and scenarios (before near-optimal
studies) have a range of $734$–$880$ bn EUR (not including existing
transmission, nuclear and hydropower infrastructure; Methods). Optimal
distributions of investments beyond solar, wind and hydrogen are given in
Supplemental Figure S1. All costs are annualised with a 7% discount rate and
given in 2023 EUR.

We model for net zero CO2 emissions and limit CO2 sequestration to 200 Mt/a
(following [28]) — this slashes natural gas use to 7% of 2021 levels [14, 9]
and renders fossil oil obsolete in the model (Supplemental Information).
Still, Europe overall can fully supply all energy demand from the residential,
services, transportation and industry sectors using only local renewable
generation, existing nuclear power and marginal use of abated natural gas.

Figure 1: An overview over the robust trade-offs between annualised onshore
wind and solar investment in Europe, consistent with the net-zero emissions
target for 2050. (a) shows the overall design space for onshore wind and
solar, with the cost slack used to compute the near-optimal space marked, as
well as the optima in the various cost- and weather scenarios marked. Note
that the optima are not necessarily robust. (b) - (c) show how the onshore-
solar space changes subject to various levels of investment in offshore wind
and hydrogen infrastructure respectively. (d) - (j) show the trade-offs
between investment in solar PV and onshore wind for the different focus
regions.

At a regional level, we observe significantly greater design flexibility
(Figure 1 (d)–(j)). In most focus regions, we can entirely eliminate onshore
wind or solar (Table 1). A number of regions need a certain minimum investment
in wind power of any kind, but the balance between onshore and offshore wind
can be adjusted relatively freely. Limited regional divestment is also
possible, though for the purposes of this study we enforce a net self-
sufficiency level of 75% for every country in the model (Methods). This self-
sufficiency requirement does not drastically increase total system cost
(Supplemental Figure S2).

Table 1: Minimal regional robust investment (in bn EUR, annualised) in the
four key technologies required for all robust designs as well as minimal total
investment in wind power (on- and offshore wind) and in renewable generation
(solar, onshore wind and offshore wind). Cells are shaded in direct proportion
to their values, with the colour scale normalised for each of the three parts
of the table independently. For example, across robust system designs Germany
requires investment of at least 19.7 bn EUR in total renewable generation, 8.3
bn EUR of which in wind power. Neither of solar, onshore or offshore wind
power on its own is strictly necessary in Germany.

Although hydrogen infrastructure (Methods) is crucial for decarbonisation and
needs investment within Europe of at least 34 bn EUR in all robust designs,
any _individual_ region can forego hydrogen infrastructure entirely. On the
other hand, we find that every studied region can become a hydrogen
powerhouse, accumulating tens of billions of hydrogen infrastructure
investment and reducing (but not eliminating) the need for hydrogen
infrastructure in the rest of the system. Across robust system designs, we
find total annual green hydrogen production in the range of about 2800–3900
TWh.

In a similar fashion, some regions may choose to export energy in significant
quantities even as all other countries cover three quarters of their demand
locally (Figure 2) — this depends on renewable energy availability. A striking
example is provided by the Nordics, which have a vast potential for wind power
exports based on annualised investment of over 230 bn EUR ($\sim$1800 GW of
onshore wind compared to currently installed 30 GW). In contrast, Germany with
its high energy demand remains an energy net importer in any robust design,
being limited by conservative assumptions on land area available for utility-
scale solar PV. Note that some of the upper ranges of the exports in Figure 2
may require subsidies using up the slack level of about 45 bn EUR.

Figure 2:  Robust ranges of net annual energy balance per focus region. All
regions can be net importers (while adhering to the 75% self-sufficiency) and
most can also be net exporters in the robust scenarios. The plot shows for
each focus region the export levels observed in 300 different randomly chosen
robust networks (Methods).

### Some technologies and combinations are locally indispensable

There are some exceptions to the wide-ranging regional flexibility, due to the
requirement to produce 75% of country-level energy demand locally. Solar
energy in Southern Europe and wind power particularly in the British Isles and
Germany are found to be indispensable (Table 1). The Nordics or France on the
other hand, with significant capacities of existing hydropower and/or nuclear
power, can meet 75% of their domestic demand with fewer additional renewables,
and without any single essential technology.

As a specific example, Figure 3 shows ranges of robust local investments in
wind power in the British Isles. We see that neither offshore wind nor onshore
power are strictly speaking necessary; either can be replaced by the other in
sufficient volume. Low investment in hydrogen infrastructure allows vast
ranges of investments in the different wind technologies (also depending on
solar investments, not shown). A strong commitment to hydrogen in the UK,
however, relies on higher investment in wind power (especially onshore) and
reduces the design space. This shows that the UK could host a large hydrogen
industry, but only in the presence of abundant renewable energy and relying on
energy exports. Overall, robust designs need at least 20 bn EUR of annualised
renewable investment in the UK and Ireland, and at least 12.3 bn EUR in wind
power — a tripling of today’s capacity [44] (Table 1).

Figure 3: Robust investments for on- and offshore wind inside the British
Isles (shaded in turquoise), depending on varying levels of hydrogen
investment (outlined with different colours) inside the British Isles.
Investments are annualised.

### Regional policies can have an oversized effect on the rest of the European
energy system

We observe cases where local investment decisions have large effects on the
robust design space of the rest of the European system. On one hand, lack of
beneficial investments in one region can lead to an inefficient overall system
design, restricting the design space. On the other hand, high regional
investment can out-compete similar investments elsewhere. A good example is
provided by the interplay between onshore wind in the British Isles and
renewable investment on continental Europe (Figure 4).

Figure 4: Trade-offs of possible robust renewable investment outside the
British Isles, depending on different levels of onshore wind investment inside
the British Isles. The full space of robust solutions is shaded in turquoise.
(a) shows the robust design space (for the rest of Europe) in the solar and
wind (on- and offshore wind combined) dimensions. The robust investments in
wind power outside the British Isles are broken down in (b) into robust
onshore and offshore wind power investments. We see that low levels of onshore
wind on the British isles push continental renewable investment (both solar
and wind) up. Very low onshore wind investment in the British Isles reduces
the overall design flexibility of the rest of the system: the 2 bn EUR level
shows a much smaller space. (See also Figure 6 showing the positive effect of
British onshore wind on continental design flexibility). At the highest
levels, on the other hand, the maximum viable wind investment in continental
Europe is reduced.

Policy decisions in some regions impact the rest of Europe not only in terms
of competition; they also significantly restrict or enable design flexibility
in the rest of the continent. Geometrically, we see that choices well within
the robust design space leave the system more design flexibility [16] and do
not force the system into narrowly bounded decisions. For example, Figure 5
shows how a boundary choice of minimal renewable generation in Germany leaves
little room to manoeuvre among remaining robust solutions, whereas allocating
an additional 35 bn EUR (4% of total system costs) to wind and solar in
Germany frees up wide ranges of robust investment choices in the rest of
Europe — despite the decrease of capital available to the rest of the system.
The strengthened investment in renewables in a central region such as Germany
affords so much robustness that it allows much greater diversity of options
elsewhere.

Figure 5: Left, the robust design space for solar and onshore wind inside
Germany, with two particular designs / points marked in brown and green.
Right, robust investment ranges for remaining technologies inside Germany and
all technologies under consideration outside Germany, at the investment levels
in onshore wind and solar inside Germany given by the two points on the left.
Green bars correspond to the green point and likewise for brown. Observe that
the investment ranges for the brown point, being located closer to the
boundary of the robust design space, are significantly smaller.

Exemplified by renewable investment in Germany, we quantify how some regional
technology investments influence the flexibility of the remaining system more
than others using the mean width of the European robust design space under
various regional investment decisions. Changes in mean width indicate how much
the design flexibility for the (remaining) European system grows or shrinks
depending on a regional investment level. This way we can single out
technologies in regions which influence the rest of Europe in a
disproportionate manner — Figure 6 shows a quantification of these
sensitivities in terms of the derivative of mean width. Generally we observe
high sensitivity to solar investment in a number of regions where solar power
plays a large role (the Iberian peninsula, the Adriatic region as well as
Germany), indicated by a high positive derivative all the way up to investment
levels of around 20 bn EUR, as opposed to low or negative impact beyond 10 bn
EUR for northern regions. This shows that a consistent commitment to solar
throughout southern Europe and Germany is needed in most robust system
designs. The relative importance of solar investment is in large part due to
the fact that all our robust system designs include a land use limitation for
utility solar at 1% of available area (having to be feasible in _all_
scenarios despite some scenarios allowing 3% in this study). This limitation
does not leave much room for compensating lacking solar investment elsewhere
(with most regions typically already close to the 1% limit) and thus raises
the relative value of additional (regional) investment in solar PV.

Generally speaking, European energy policy is less sensitive to onshore wind
investment in any particular region of interest, with only Germany and the
British Isles presenting moderate impact. This lower sensitivity indicates
that onshore wind investment is more easily shifted geographically and other
regions can compensate higher or lower investment. Although spatially
flexible, wind power in Europe is a key system component with 165 bn EUR
minimum investment (at least 58 bn EUR for onshore wind) for any robust
design.

Figure 6: An overview of how regional investment decisions affect the design
flexibility of the rest of the European system in terms of derivative of mean
design space width. The levels of regional investment leading to maximal
outside flexibility (where the derivative is zero) are marked with black
vertical bars. On either side, the derivative of mean width of the robust
design space outside the given focus region, with respect to regional
investment in solar, onshore- and offshore wind and hydrogen, is indicated
using a colour scale. A positive derivative indicates that additional marginal
investment in a given technology (inside a focus region) enlarges the design
space, thus the flexibility, outside the focus region. For each region and
technology, the mean derivatives up to maximum outside flexibility and beyond
this point (which are positive and negative respectively) are annotated. For
instance, investment in solar in Poland and the Baltics has a positive
effective on design flexibility in the rest of the system from 0 and up to
about 14 bn EUR, with a mean derivative of 3.2 over this range. Robust onshore
wind investments in the Nordics are cut off at 130 bn EUR (Figure 1(e)). Note
that the mean design space width can be sensitive to narrow ranges of possible
robust investment (such as offshore wind in Iberia). Supplemental Figure S3
shows the “converse” to this figure, with inside and outside dimensions
swapped.

### European policy sets the limits for regional energy design space

Conversely, regional investment decisions are sometimes also strongly impacted
by policies in the rest of Europe. This in itself is not surprising, as
today’s transmission interconnection levels are already high (here we restrict
transmission expansion to 25% on top of current levels, even if more could be
cost-efficient [4, 37]) and additional energy transportation is enabled in the
model through hydrogen and gas pipelines. We generally see two distinct
effects: strong European investment limits most individual regions’ potential
for becoming major energy exporters, whereas weak European investment can
force some regions to compensate.

Figure 7: Minimum and maximum potential ranges of total wind power investment
in different regions, as a function of wind power investment outside the
respective regions. In all cases, “wind power” means onshore and offshore wind
combined. Note that each subplot represents separate results from differently
focused models, hence the disagreement on maximum overall viable wind power
investment. Supplemental Figures S4–S5 show the corresponding regional
potential of solar and hydrogen investment, respectively.

Figure 7 illustrates both effects. The massive potential for wind power
development in both Poland and the Baltics as well as in the Nordics decreases
steadily with rising wind investment in the rest of Europe. At the same time,
each of these two regions is individually forced to compensate strongly if the
respective rest of the system falters in wind power. This dynamic results from
low domestic demand but plentiful wind resources making large-scale wind
development generally export-dependent and thus sensitive to outside
developments. The British Isles and especially Germany, however, have
significant need for wind investment almost regardless of the wind development
elsewhere; this is likely due to strong domestic energy demand. These regions
stand apart as requiring the highest minimum investment in wind power across
_any_ robust system design (Table 1). The British Isles also have the
potential to export wind power and this exposes local wind investment to some
competition, but their investment is never completely out-competed by
continental wind investment — possibly due to its high wind capacity factors
and peripheral location.

### Discussion & Conclusions

We demonstrate that within an integrated European energy system, single
countries or regions have large flexibility in designing their contribution to
joint decarbonisation policies. Trade-offs and broad ranges of options have
been previously shown for the European electricity sector[27, 34], and play
out even stronger for individual regions. Although certain minimal investments
in specific renewable generation are required, we show that most single
technologies can be substituted.

However, the design space of individual regions does not exist in a vacuum but
is strongly coupled with the surrounding system. We consistently see that
transmission expansion is cost-efficient and the coupling between regions is
only expected to deepen due to benefits of increased transmission capacities
[37, 4, 18, 42] as well as a hydrogen pipeline network [28]. The interaction
between national and continental policies means that both sides can increase
or decrease the extent of the design space of the other, respectively. For
instance, higher investment in solar in Southern Europe and Germany expands
the design flexibility of the rest of Europe. A strong commitment to wind
power in Poland and the Baltic countries shrinks the ranges of possible wind
investment elsewhere and generates import dependencies for the rest of the
system. In general, investment in wind power and hydrogen infrastructure can
be shifted geographically rather freely, but solar power less so.

Conversely, we show the extent to which energy policy in individual countries
and regions, while flexible, is affected by the direction of the rest of the
system. Any of the studied regions can be energy net importers (or exporters,
except for Germany), but not all at the same time. Northern Europe has
significant potential for wind-based exports, but this potential can be
rendered largely unprofitable if the renewable investment is strong in the
rest of Europe. The EU as well as individual countries have come forward with
hydrogen strategies in recent years [11, 38, 5, 30], and our results show the
need for a minimum annualised investment of 34 bn EUR in the European hydrogen
sector by 2050; however, _where_ these investments occur is very flexible. All
in all, neither individual countries nor the EU can plan the transition to
net-zero emissions without taking the tapestry of energy strategies across the
European continent into account.

We find a vast space of robust designs achieving net-zero emissions as well as
a high degree of energy self-sufficiency even under multiple challenging
weather years, pessimistic technology cost assumptions and strict land use
restrictions. While we attempt to strike a conservative balance in this study,
the extent of this space does depend on the set of scenarios under which each
design must be feasible. We choose scenarios reflecting a mix of
meteorological, technological and societal uncertainty, but this set of
scenarios is more of a starting point than a canonical selection. Weather
years have already been identified as having a major impact on the energy
system design space [16], and the present study reveals land use restrictions
for utility solar power as another critical factor. Including scenarios with
allowances of both 1% and 3% of available land, we see that this socio-
political limitation cuts down the space of robust system designs in a drastic
way. The impact of emissions targets, strengthened interconnections and demand
response on the extent of design flexibility, to name a few, are not yet
explored.

Although beyond the scope of this article, it is conceivable that early
adopters [43] of key renewable technologies may benefit insofar as they can
shape the design space and set the agenda of the rest of Europe and force
later investments to be of a more reactive nature. Here, multi-horizon
modelling and a study taking several regions into account simultaneously could
be of great value to policymakers. Furthermore, computational limitations
restrict us to mapping out the design space in only 8 key variables at a time.
Finding ways to take more variables (regions, technologies) into account could
prove fruitful.

The vast planning flexibility we demonstrate underlines the agency of single
regions and countries in shaping energy policy: if onshore wind is socially
unacceptable, for example, many regions can substitute it with other
technologies. On a continent with different transition speeds [24] and levels
of ambition [40], almost all countries have the possibility to benefit from
building up new industries through electricity or hydrogen exports. However,
certain trade-offs between regions are unavoidable and must be considered in
light of social and political priorities that are difficult to quantify. To
overcome opposition to climate mitigation and strengthen a fair energy
transition, accounting for diverging interests in a panoply of pathways is
possible and necessary.

## Methods

### Modelling framework

For this study, we use the open-source energy system model PyPSA-Eur-Sec 0.6.0
[4] (since merged into PyPSA-Eur) which represents the European energy system
including the power, heating, industry, transport and agricultural sectors. It
includes a detailed representation of the existing electricity transmission
and gas networks, as well as generation sites and spatially resolved demand of
different sectors. With the aim of a 100% emission reduction in the European
power, heating, transportation and industrial sectors, the model finds
investment and operational decisions for generation, transmission and storage
in order to minimise total annualised system costs and meet projected 2050
energy demand.

Estimates of fixed and operational costs for 2050 are taken from
https://github.com/PyPSA/technology-data, a repository collecting cost data
and learning curves from various sources. All capital costs are annualised
with a discount rate of 7%; this discount rate is chosen because it is the
default in PyPSA-Eur, hence making the results more directly comparable across
studies. While costs in the above repository are given in 2015 EUR, we have
converted all cost data to 2023 EUR for the purposes of this study, using
inflation data for the Euro area up to October 2023 [13], amounting to a 24.5%
increase compared to technology-data.

The model is run with a partial greenfield approach, where existing
transmission and gas networks (2019) as well as nuclear (except for Germany),
biomass, and hydropower generation (2022) are included at today’s capacities.
The above infrastructure was included because of its relatively long lifetime
(including potential lifetime extensions), making existing capacities likely
to approximately persist until 2050. The gas and transmission networks may
additionally be reinforced beyond today’s capacities in the model; for
transmission this is limited to 125% of current levels. Nuclear, biomass and
hydropower generation, on the other hand, are entirely fixed (i.e. not subject
to optimisation) and are not included in total system costs.

The main technologies whose expansion is optimised from scratch include solar,
onshore wind and offshore wind generation, gas turbines, combined heat and
power plants with and without CCS, boilers, battery-, hydrogen and heat
storage, various power to X and other energy conversion technologies
(electrolysis, steam methane reformation, methanation of hydrogen, ammonia and
methonol production from hydrogen, synthetic fuel generation, biogas), direct
air capture and carbon sequestration. The model includes all major potential
components of a European energy system anno 2050, including the electricity,
heating, transportation and industry sectors. See the accompanying code and
data as well as PyPSA-Eur documentation and a recent study on the potential of
a European hydrogen network [28] for more details.

We choose a spatial resolution of 60 nodes for 33 European countries, however,
the exact allocation of nodes varies between the differently focused models
(see below). In order to reduce the computational burden further, we use a
non-uniform time step aggregation [35, 21] with 1500 time segments (which has
shown to be more accurate than a comparable 6-hourly time resolution).

For all countries represented, we impose a 75% net self-sufficiency constraint
for annual energy demand. It prevents the unnecessary exploration of
technically robust system designs where individual regions are heavily
dependent on imports — we consider such designs unlikely to be realised. At
the same time, it can be seen as a measure to strengthen energy security and a
more equal burden between different European countries in the joint
decarbonisation efforts. The implementation of such a self-sufficiency
constraint is a novelty in the context of sector-coupled energy system models
for Europe; previously this was merely implemented for the electricity-only
version of the model (PyPSA-Eur). The constraint is implemented bounding the
ratio between total yearly local energy production and total yearly energy
imports.

### Regional studies

Our results are based on studying the joint space of robust system designs of
the European energy system, reduced to total investment in four key
technologies both inside and outside 7 selected focus regions. For the
approximations of these 7 robust design spaces, we use the same model of the
European energy system, except that we distribute the spatial nodes of the
model differently in order to allocate more spatial resolution to each
respective focus region. Moreover, we also allocate slightly more nodes to
countries neighbouring each focus region. Our focus regions are

  * •

Poland and Baltics (EE, LT, LV, PL) with 20+25+15 nodes,

  * •

Nordics (DK, FI, NO, SE) with 20+25+15 nodes,

  * •

Adriatic (AL, BA, GR, HR, IT, MT) with 30+20+10 nodes,

  * •

Germany (DE) with 20+25+15 nodes,

  * •

France (FR) with 20+25+15 nodes,

  * •

British Isles (IE, UK) with 15+25+20 nodes,

  * •

Iberia (ES, PT) with 20+15+25 nodes,

with the corresponding number of nodes inside the region, for neighbouring
countries and for remaining countries (further removed than distance 1),
respectively. The increased spatial resolution inside the focus region allows
us to capture renewable potential and effects like transmission bottlenecks in
better detail. See Supplemental Figure S6 for a visual representation of the
networks.

### Scenario selection

For each focus region, we consider different scenarios across input
uncertainties that we deem particularly impactful on energy modelling results.
For each of these scenarios (and for each focus region), we approximate the
corresponding near-optimal feasible space using the methods introduced by
Grochowicz et al. [16]. For each focus region, then, we consider as robust
design space the _intersection_ of the near-optimal spaces arising from the
scenarios under consideration (see below).

The factors we vary across scenarios and which we consider most impactful to
modelling results include weather years [45, 16], cost assumptions[27], and
land use[31] availability. Following Grochowicz et al. [16], we select three
weather years that are considered difficult (1985, 1987, 2010) and thus are
particularly restrictive (and also significantly more expensive than other
weather years). We define three cost scenarios, one “baseline” scenario with
standard cost assumptions, and two scenarios with higher capital expenditure
costs for solar PV (39% more expensive) and wind power (24% more expensive)
respectively; these ranges are taken from cost projections by the Danish
Energy Agency [7]. Lastly, we restrict the available land area for utility
solar PV in comparison to the standard assumptions in PyPSA-Eur-Sec to one
third (from 3% to 1% of available land area after excluding unsuitable areas
[19]). The restricted land availability scenario inhibits expansion of solar
PV significantly: for instance, Germany’s installation potential is capped at
approximately 440 GW while the German government is targeting installed
capacities of 400 GW until 2040 [15]. All in all, this gives us $12$
scenarios, as we pair the three different weather years with the three cost
scenarios and the restriction on land use for utility solar
($3\cdot(3+1)=12$).

### Design spaces

The design space for each of the above scenarios and focus regions, consists
of feasible, alternative solutions to a cost-optimal solution which can be
preferable over the cost optimum for other reasons. Energy system optimisation
models are usually formulated mathematically as linear programs of the form
$\min cx\text{ subject to }Ax\leq b$ in which case the _design space_ , more
formally _$\varepsilon$ -near-optimal feasible space_ [8, 26, 16], is defined
as $\mathcal{F}_{\varepsilon}=\\{x\in\mathbb{R}^{n}\mid Ax\leq b\text{ and
}cx\leq(1+\varepsilon)\cdot c^{*}\\}$ where $c^{*}$ is the optimal objective
(minimum cost) of the original linear program.

For the purposes of this study, we use a cost slack of $\varepsilon=5\%$.
However, for each focus region we compute a uniform cost bound for all
scenarios based on the optimum system cost for the most expensive scenario
(roughly following [16]). More precisely, let $r$ be a region and $S$ a set of
scenarios, such that we get a linear program $A_{r,s}x\leq b_{r,s}$ with
objective $c^{*}_{r,s}$ for each $s\in S$. Then we define the near
$\varepsilon$-near-optimal space for scenario $s$ as

$\mathcal{F}_{\varepsilon}^{r,s}=\\{x\in\mathbb{R}^{n}\mid A_{r,s}x\leq
b_{r,s}\text{ and }c_{r,s}x\leq(1+\varepsilon)\cdot\max_{s^{\prime}\in
S}c^{*}_{r,s^{\prime}}\\}$

Defining near-optimal spaces for a set of scenarios as above allows for more
direct comparisons, since all spaces are defined with respect to same absolute
bound on total system costs.

In models of similar size to PyPSA-Eur-Sec (with $n$ significantly greater
than $10^{6}$), the design spaces which can be analysed effectively are
projections onto a few key dimensions from the high-dimensional space
$\mathcal{F}_{\varepsilon}^{r,s}$. This is because an accurate approximation
of such a design space is computationally demanding (one vertex is obtained
through one optimisation of the linear program) in high dimensions [33, 16].
Following previously introduced notation [16], we consider the reduced, low-
dimensional design space
$\mathcal{A}^{r,s}_{\varepsilon}\subset\mathbb{R}^{k}$; related to the full-
dimensional space by a linear map
$\sigma\colon\mathcal{F}_{\varepsilon}^{r,s}\to\mathcal{A}_{\varepsilon}^{r,s}$.
In our case, we map down to $k=8$ key dimensions: the total investments
_inside_ and _outside_ the focus region in utility solar, onshore wind,
offshore wind, and hydrogen infrastructure. Hydrogen infrastructure
investments consist of investment in electrolysis, fuel cells, pipelines (both
new and retrofitted from existing gas pipelines), synthetic methane and fuel
production from hydrogen (methanation, Fischer-Tropsch process respectively)
and steam methane reforming plants (with or without carbon capture) as well as
hydrogen storage.

An accurate approximation of the design space geometry can inform policymakers
about trade-offs between regional and continental investment, alternative
technologies, and how much flexibility can be gained through the introduction
of a cost slack of $\varepsilon$. For a more detailed description of the
approximation methodology and validation see [16]; in this case, we conduct
450 optimisations for a satisfying approximation of each design space. See
Supplemental Figures S7–S8 for a visualisation of the individual near-optimal
spaces as well as their intersection for one of the focus regions.

### Robust solutions and design flexibility

To find solutions that are feasible (and near-optimal) notwithstanding the
uncertainties encoded in our selection of scenarios, we look for investment
decisions that lie in the feasible design space for each scenario. We formally
define the space of _robust solutions_ (or energy system design) as points in
$\mathbb{R}^{k}$ that lay within the intersection of the reduced design spaces
for every scenario $s\in S$ under consideration:

$\mathcal{I}_{\varepsilon}^{r}=\bigcap_{s\in
S}\mathcal{A}_{\varepsilon}^{r,s}.$

We refer to [16] for an extensive overview of the intersections of near-
optimal feasible spaces with all due details.

By considering the geometry of the space of robust solutions (as in Figures 1,
3 and 4, for example), we are able to study trade-offs between investments in
different technologies both inside a given focus region and in the rest of
Europe. One should keep in mind that the formulation in terms of near-
optimality adds a slack of 5% on top of the optimal total system costs which
corresponds to an additional investment of around 45 bn EUR (depending on the
focus region) which can be allocated in different ways in order to enlarge the
alternative robust options. Note that monetary investments are robust across
scenarios, however they might translate to different capacities in the
scenarios with higher costs for solar PV or wind power.

To compute export potential, shown in Figure 2, we need a representative
sample of full system designs (including operations) laying inside
$\mathcal{I}_{\varepsilon}^{r}$ for each region $r$. This is because the
geometric shape of $\mathcal{I}_{\varepsilon}^{r}$, which we compute as an
intersection of near-optimal spaces, only contains information about total
investment in solar, onshore wind, offshore wind and hydrogen (inside and
outside $r$), but no total export figures. Thus, for each $r$, we sample 300
points in $\mathcal{I}_{\varepsilon}^{r}$, and run model optimisations where
total solar, onshore wind, offshore wind and hydrogen investment are fixed to
the coordinates of the 300 points. We can then calculate total imports /
exports for each model and region; the results are shown in Figure 2. The 300
points are sampled randomly on the boundary of
$\mathcal{I}_{\varepsilon}^{r}$, except the first 24 which consist of those
points which min- and maximise each individual of the 8 key dimensions (16
total) and those that min- and maximise the system-wide solar, onshore wind,
offshore wind and hydrogen dimensions (8 total).

For Figure 6, we use _mean width_ as a simple metric for measuring the size of
a design space, and thus as a quantification of design flexibility. The notion
of mean width we use for the purposes of Figure 6 is the mean of the widths of
the space in the 4 outside investment dimensions. In other words, for a given
inside investment level (say, a 10 bn EUR investment in onshore wind in the
Nordics), we compute outside design flexibility as the mean of the differences
between maximum and minimum outside investment in solar, onshore wind,
offshore wind and hydrogen.

By varying technology investment levels _inside_ a focus region we capture the
increasing or decreasing mean width of the projection onto European
investments _outside_ the focus region. These increases and decreases of
flexibility are shown as derivatives in Figure 6.

## Code and data availability

The code to reproduce the results of the present study, as well as links to
the data used, are available at https://github.com/koen-vg/enabling-
agency/tree/v0. All code is open source (licensed under GPL v3.0 and MIT), and
all data used are open (various licenses).

## Acknowledgements

A.G., F.E.B. and M.Z. acknowledge funding by UiO:Energy and Environment
(SPATUS).

ERA5 reanalysis data [17] were downloaded from the Copernicus Climate Change
Service (C3S) [6].

The results contain modified Copernicus Climate Change Service information
2020. Neither the European Commission nor ECMWF is responsible for any use
that may be made of the Copernicus information or data it contains.

## Declaration of interests

The authors declare no competing interests.

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