# The trade-off between socio-environmental awareness and renewable penetration targets in energy transition roadmaps

Aina Maimó-Far, Víctor Homar, Alexis Tantet, Philippe Drobinski

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Aina Maimó-Far, Víctor Homar, Alexis Tantet, Philippe Drobinski. The trade-off between socio-environmental awareness and renewable penetration targets in energy transition roadmaps. Applied Energy, 2024, 355, pp.122397. 10.1016/j.apenergy.2023.122397. hal-05345191

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# The trade-off between socio-environmental awareness and renewable penetration targets in energy transition roadmaps

Aina Maimó-Far<sup>a,*</sup>, Víctor Homar<sup>a</sup>, Alexis Tantet<sup>b</sup>, Philippe Drobinski<sup>b</sup>

<figure><img src="image_3.png" /></figure>

## GRAPHICAL ABSTRACT

The trade-off between socio-environmental awareness and renewable penetration targets in energy transition roadmaps

<figure><img src="image_4.png" /></figure>

System total cost minimization uses system components in economic terms to find optimal solutions

<figure><img src="image_5.png" /></figure>

The best trade-off taking a nexus approach does not stand out in any of the silo indicators

<figure><img src="image_6.png" /></figure>

Official development plans are aligned with a balanced approach which gives the best nexus results

Aina Maimó-Far, Víctor Homar, Alexis Tantet, Philippe Drobinski

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

Universitat
de les Illes Balears

## ARTICLE INFO

MSC:

46N99

Keywords:

Renewable energy deployment

Land sustainability

Land-energy nexus

Sustainable development goals

Ecosystem services

Energy system cost

Multi criteria decision analysis

## ABSTRACT

Recent years have seen Sustainable Development Goals mark the way towards a sustainable future and put the growth of renewable energy sources in the spotlight. This increase, led by PV and wind technologies, will be necessary to meet renewable penetration targets in upcoming decades. However, these sources require vast amounts of land, a limited resource affecting other Sustainable Development Goals such as ecosystem protection or food production. This article explores the land-energy nexus through the minimization of the system total cost that incorporates a form of suitability for land occupation. Three differentiated regimes appear under a changing suitability cost, with a gap of 70% penetration between the two extremes, and with very high suitability costs unable to meet future objectives given their cap at around the 35% penetration mark. The intermediate approach presents the best fulfillment of Sustainable Development Goals overall, with an increase between 15 and 30% with respect to the other regimes. Existing development plans for the Spanish system point towards this midway approach, a sign of their commitment to sustainability. This study shows that a balanced consideration of land and energy should be prioritized, as the negative effects that arise in a biased approach outweigh the benefits.

<footnote><sup>a</sup> Meteorology Group, Physics Department, Universitat de les Illes Balears, Cra. de Valldemossa, km 7.5, Palma, 07122, Spain</footnote>

<footnote><sup>b</sup> Laboratoire de Meteorologie Dynamique/Institut Pierre-Simon Laplace, École Polytechnique, IP Paris, Sorbonne Université, ENS, PSL University, CNRS, Rte de Saclay, Palaiseau, 91120, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: aina.maimo@uib.cat (A. Maimó-Far).</footnote>
# 1. Introduction

Sustainability has long been a subject of extensive study, capturing the attention of decision-makers and researchers alike. Despite a general consensus on the desirability of a sustainable future, the exact definition of sustainability remained elusive. In a significant development, the United Nations (UN) in 2015 reached a consensus by establishing seventeen Sustainable Development Goals (SDGs). These SDGs delineate the areas of concern for sustainability, encompassing a wide range of topics, from ecosystem preservation to poverty alleviation and gender equality (United Nations, 2015). Importantly, each SDG is accompanied by a set of subgoals and indicators, facilitating a more precise measurement of progress toward these goals.

One SDG that stands out and serves as the primary focus of this work is SDG 7: affordable and clean energy. This goal emphasizes the universal access to affordable and dependable energy, sourced sustainably and from modern technologies. However, the expansion of renewable energy sources necessitates additional land use, which competes with other SDGs that also require land for their realization. This dynamic underscores how advancements in the energy sector can potentially constrain the pursuit of other SDGs, given the finite nature of land as a resource.

Assessing energy development while considering its intersection with other SDGs necessitates a comprehensive examination of energy and its impact on land. In recent decades, there has been a paradigm shift toward viewing relevant factors as interconnected systems rather than isolated components. This holistic approach, known as the nexus approach, has found widespread application in recent decades. Most of its applications have focused on the Water-Energy-Food nexus [1] to identify synergies between the subsystems, although additional considerations include the addition of ecosystems [2], the replacement of food in favor of the environment [3] or climate [4], the joint consideration of food and climate together with energy and water [5] or sometimes only consider other factors, such as energy and land [6]. Even though the consideration of land inside a nexus only dates to recent years [7], it is a fundamental element to consider when exploring renewable energy deployment.

In this article we explore the land-energy nexus, which can be related to two main perspectives: the ecological modernization, and the spatial justice [6]. Nowadays, it is widely accepted that renewable energy is a necessary element in the transition towards a lower-carbon future [8], but its expansion generates conflicts [9]. These technologies require more land than their non-renewable counterparts, and there is an existing concern regarding the land availability for renewable sources [10], especially in the context of ambitious renewable penetration scenarios [11]. From this concern stem the two mentioned perspectives. On the one hand, the ecological modernization perspective focuses on the necessity to solve present and future climate and energy problems. This is the perspective followed by government institutions in their large-scale planning, and it focuses on wide objectives. However, these large-scale goals do not necessarily analyze the impacts of the required installations on their local vicinity. From these types of concerns stems the spatial justice perspective, which concentrates on the spatial distribution of these resources, and the potential negative impact of the renewable energy installations on the rural scenery [12] and on the livelihood of local [13] and especially rural [14] communities. Given this dichotomy, balancing the need for renewable energy integration and the limited land available with its limitations is essential to identify viable future developments.

In the context of a renewable energy-land nexus, it becomes fundamental to assess the trade-offs that occur between these two components. For instance, areas with tourism-based economies require strong seasonal energy generation, but in turn need to preserve certain land use and landscape standards [15]. Land use change to the deployment of energy infrastructures may also affect the local climate

through change in albedo and evaporation [16]. Similarly, but considering greenhouse gas emissions, [17] explore this three-way nexus in the context of shared socioeconomic pathways. In a more direct application, [18] explored the link between wind energy, biodiversity, and land use to assess the more sustainable and less invasive approaches, finding a viable scenario that meets the ambitious national goals while avoiding installation on natural protected spaces and minimize ecosystem and habitat fragmentation.

The renewable energy-land nexus is mostly described qualitatively in the existing literature, despite both parts of this nexus having been widely addressed quantitatively [6]. Additionally, quantitative approaches to the nexus in the existing literature take one of two approaches: either condition the energy deployment to land availability or explore the impact of energy deployment on land services. However, these two mechanisms are simultaneous, and therefore should be considered as such. The present work proposes a study of the nexus between land and renewable energy that incorporates ecosystem services to assess the value of occupied terrain. To do so, a pseudo-cost is assigned to land occupation, and is then handled simultaneously with the cost of renewable installations and dispatchable generation, therefore considering the effect of land on energy deployment and vice versa. This is done through an economic cost-based optimization, which has been used in existing studies for applications such as the assessment of new generation sources under uncertainty [19], the integration of wind energy in a grid [20] or the estimation of long-term economic value of renewable generation sources [21]. We focus on utility-scale solar photovoltaic (PV) and onshore wind energy, as they are the variable renewable energy (VRE) sources that generally present the cheapest generation costs [22], despite their strong variability, which can make other technologies such as hydropower cheaper in individual instances [23]. Additionally, PV and wind currently represent the two fastest growing technologies, but their land occupation is among the largest [24], which puts forward the importance of ensuring that land is being used sustainably for the siting of capacity [25].

Ecosystem Service Values (ESV) allows us to assign an economic value to the land as a quantification of the goods, services and functions provided by its ecosystem [26], while keeping in mind its need for protection [27]. This consideration will allow for a comparison of the cost of occupying the land to the cost of installing renewable energy sources. Multiple approaches have used an ESV approach to establish a price for the occupation of land [28], which has only grown with time [29] but still maintains strong variability depending on the specific valuation [30]. It should be noted that any assessment of the economical value of land will likely not correspond to a market price, omit some costs associated to indirect services [31], and that any ESV procedure remains a simplification [32].

In this study, we propose an ESV approach to the occupation of land by PV and wind energy sources, and integrate it with the cost of energy in a description based on economic cost of the land-energy nexus and its internal trade-offs, and then apply it to the sample case of Spain. The case study of Spain, its electricity system and general land occupation is presented in Section 2. Section 3 introduces the main data and methods used, and describes the proposed approximation to the ESV quantification in a renewable energy-land nexus context. In Section 4 we analyze the results of the trade-offs on renewable energy deployment scenarios. The corresponding impact of the nexus approach on the environment and the associated real-world Spanish development plans and United Nations SDGs are presented and discussed in Section 5. Finally, Section 6 presents the main conclusions from this study and expands on its policy implications.

# 2. The Spanish electricity system

The case study chosen to delve into the delicate balance between energy generation and other land uses for sustainable development is Spain. This section offers an overview of the key features of the Spanish
electricity system, drawing from the official report for the year 2022 covering the entire system [33], with a specific focus on renewable energy sources [34].

Renewable energy sources constitute a substantial portion of the energy landscape in Spain, accounting for 59.2% of installed capacity. However, they contribute to only 42.2% of the total energy generation. To break it down further, wind and photovoltaic (PV) energy represent 25.2% and 16.6% of installed capacity (22.1% and 10.1% of generation), respectively (see Fig. 1 top). Hydropower, while boasting 14.4% of installed capacity, contributes only 6.5% to energy generation.

Wind and PV energy sources are widely recognized as the driving forces behind Spain's transition toward renewable energy. Over the past decade (2013–2022), their capacity has surged by over 30% and 350%, resulting in generation increases of 10% and 235%, respectively. In stark contrast, hydropower has seen a modest 15% increase in installed capacity but a staggering 45% decline in generation. This decline in hydropower is not only influenced by the ascendancy of wind and PV but also by the persistent water scarcity issue in Spain. Rainfall has exhibited a declining trend for several decades [35], a trend expected to continue [36].

The concern over water availability extends beyond its impact on hydropower. The majority of Spain's land is dedicated to agriculture and natural vegetation, both of which are vulnerable to reduced precipitation. While most of the Spanish population resides near the coasts and in the central capital, leaving a significant portion of the territory for agriculture and nature, the potential uses for this land are diverse. In this article, we will delve into the various land uses, as the advantages or disadvantages of relinquishing a parcel of land for renewable installations can vary greatly depending on the specific use.

Taking all these factors into account, the utilization of some land for energy generation becomes an inevitable necessity if energy demand is to be met. Meeting electricity demand poses a particular challenge, especially during the summer months (and to a lesser extent, winter) when cooling or heating systems are essential for maintaining comfortable temperatures. However, when considering overall energy consumption, transportation accounts for 44%, followed by industry at 24%, home consumption at 17%, and the service sector at 12% [37]. The majority of this energy demand is still met by fossil fuels, especially in transportation and industry. Hence, electricity demand is poised to increase as electrifying these sectors becomes imperative for emissions reduction.

Spain's current energy landscape has been shaped by successive objectives, closely aligned with the European Union's (EU) renewable energy goals. In 2018, the EU [38] set a target of achieving a 32% renewable energy penetration across the European Union by 2030, leading to Spain's objective of 42% penetration in its 2021–2030 plan [39]. As Spain adapts to climate change, research into renewable deployment gains prominence [40], prompting continuous upward revisions of renewable penetration objectives. The EU's initial target was raised to 45% in 2022 [41], and in alignment with this, Spain's goal was further expanded and detailed in the development plan by Red Eléctrica de España (REE), the Spanish operator [42], projecting an estimated penetration of 50% (see Fig. 1 bottom).

Spain's case is particularly intriguing due to its abundant climatic resources, yet it lags behind many other EU countries in terms of clean energy adoption [43]. However, substantial commitments are being made, with over €240 billion earmarked for the energy transition in the current decade, of which €90 billion is dedicated to renewable energy deployment [39]. Spain demonstrates a strong commitment to clean energy in the coming decades, and this work aims to provide guidance for achieving sustainable development in the realms of both land use and energy.

### 3. Methodology

The starting point for the methodology developed in this work is the system total cost minimization problem, fully developed in [44]. In this approach, given a distribution of VRE installed capacities $x$, with $x_i$ the installed capacity for each combination $i$ of region and technology from a total of $m$ combinations. Additionally, conventional generation sources are handles as aggregated dispatchable generation. Under the assumption of a perfect market and a merit-order effect (i.e. conventional sources enter the mix in order, starting from the cheapest option, and with cost increasing linearly), the total cost of dispatchable generation is proportional to the square of the dispatchable generation. Therefore, the one-year system total cost (STC) given a parameter $\alpha$ for the cost of dispatchable generation is defined as

$$STC_a(x, q) = T_0 \sum_{i=0}^{m-1} hRC_i x_i + \alpha \sum_{i=0}^{T_0-1} q^2(t), \quad (1)$$

with the first term being the cost of VRE installation and the second term representing the cost of dispatchable generation. The cost of VRE installation only depends on the capacity installed ($x_i$) and the hourly rental cost of such installations (hRCi), with $T_0$ being the number of hours in a year, used to convert hourly rental cost into the yearly total. The cost of dispatchable generation is assumed to be quadratic on the energy generated ($q_i$), and weighed by a non-negative coefficient $\alpha$ that ponders the relation between the cost of VRE sources and dispatchable sources, and which can be related to the market price of electricity (under the assumption of a perfect market) through the marginal cost.

Given a mix of VRE, the renewable generation can be defined as

$$Q_x(t) = \sum_{i=0}^{m-1} x_i H_i(t), \quad (2)$$

with $H_i(t)$ the time series of capacity factor at point $i$. By having definitions of renewable generation $Q_x$ and dispatchable generation $q$, we can define the condition for energy supply adequacy given a demand (or load, $L(t)$) as

$$\begin{gathered} q(t) + Q_x(t) \ge L(t) \\ 0 \le q(t) \le x_{Di} \\ \forall t \in 0, \dots, T_0 - 1, \end{gathered} \quad (3)$$

with $x_{Di}$ the dispatchable installed capacity. In optimal solutions, by construction, dispatchable sources only enter the mix when VRE sources do not cover the electricity load, otherwise their production is set to zero. Therefore, demand is guaranteed to always be covered by the sum of dispatchable production and VRE generation. Under these constraints, the optimization problem is well defined. The optimization problem to characterize the optimal VRE deployment is

$$\begin{gathered} \min_x \mathbb{E}(\text{STC}(x)) \\ \text{s. t. } 0 \le x_i \le x_i^{\text{max}}, i \in 0, \dots, m-1, \end{gathered} \quad (4)$$

with $\mathbb{E}$ the expectation, STC the set of yearly STC over a sample of multiple years and $x_i^{\text{max}}$ the maximum installable capacity for a region and technology pair $i$.

The presented framework defined a simplified STC-based optimization problem using e4clim under the mentioned assumptions of dispatchable generation shape and no transmission-derived costs. This optimization is performed at the climatic grid scale (i.e., over the ERA5 grid, considering the climatic grid boxes as the regions over which capacity is optimized) as a compromise between the various spatial scales from the different data sources used, which include data from a 100-meter mesh, to the municipality, autonomous community, and even national scale. In order to solve the optimization problems, the Pyomo [45,46] interface and the Ipopt [47] algorithm are used as designed in Tantet and Drobinski [44]. In this study, we introduce a new term to the STC definition related to the suitability of land for renewable installation and analyze its impact on the resulting optimal scenarios.
<figure><img src="image_9.png" /><figcaption>Fig. 1. Spatial distribution of installed capacity at the end of 2020 (top) and Spanish development plan installation (bottom) for PV (left) and wind (right). Line divisions represent autonomous communities. In the bottom panels, the capacity (MW) installed in each autonomous community is annotated.</figcaption></figure>

## 3.1. Estimation of suitability cost and land availability

Suitability cost is not a unique empirical magnitude. Its estimation requires relying on expert assessment, as evidenced by the literature. In this article we provide an estimate that encompasses the most relevant factors that affect the social, economic and environmental impacts of VRE deployment. In order to assign an economic cost to the suitability of installation, we need to turn to ESV. The first step towards considering the suitability of specific locations for VRE installation in the optimization problem is to diagnose how much land is available for installation and how suitable the available land is. We follow the framework of ESV in combination with the Geographical Information Services (GIS) and Multi Criteria Decision Analysis (MCDA) for two different assessments: whether VRE technology can be installed or not in a given area, and how costly that installation would be in economic, social, and environmental terms. We conduct these two assessments over 100-meter square pixels and analyze whether a given pixel can hold VRE technology and, if so, how suitable it is. This information propagates to the climate-grid scale for the optimization in the form of a constraint to the maximum occupiable surface and a parameterization for the suitability.

The process of creating a unique measure for suitability follows technical, economical and sustainability reasoning. However, these three factors are strongly interlinked, and their effects on suitability are always consistent. From the sustainability point of view, the SDGs [48] establish a reference for some relevant factors to consider. In the present article, the main goals that are addressed are SDG2 (Zero hunger), SDG7 (Affordable and clean energy), SDG13 (Climate action), and SDG15 (Life on land). Further reference to the specific indicators of each SDG will be mentioned along the article.

### 3.1.1. Land availability estimation

Our analysis of land availability entails evaluating the suitability of each pixel hosting VRE installations, taking into account restrictions, both legal and practical. In instances where legal restrictions

are present, the pixel is immediately considered incompatible with VRE installation. Conversely, if no legal restrictions apply, we employ a systematic evaluation process based on established criteria in the literature to assess the aptitude of the land for accommodating VRE installations.

The following criteria (and some references to the existing literature that use them) are used to discard a pixel as available for installation:

* Natural protected areas (limited by Spanish regulation, also as in [49–51])

* Floodable areas or hydrological features, areas under 500 m from the coastline (limited by Spanish regulation, as in [52–54])

* Areas under 3 km from airports (as in [55–57])

* Areas with unsuitable land use such as water bodies, urban or ice-covered areas (see Section 3.1.2 for the exact approach to land use; as in [58–60])

After applying these criteria, all pixels are labeled either as available for installation or not. Therefore, we know the exact area available for installation in each climatic grid box. Since the already-installed capacity is taking up surface that may be discarded by the land use constraint, we add the surface already taken up by present renewable installation (at the end of the reference year 2020) in order to assure that existing installations can be considered in each grid box. This area will be applied in the optimization problem as a constraint on the maximum occupied surface. All of these processes are made using the relationship between installed capacity and land occupation explained in Appendix A (in this study, we use 0.2 km²/MW for wind, and 0.02 km²/MW for PV).

### 3.1.2. Suitability index

For each 100-meter pixel, we define a suitability index. This index includes implicit information regarding the cost of installation and maintenance associated to the terrain and its accessibility and the economic cost of construction, both of them indirectly linked to SDG7.3 (by 2030, double the global rate of improvement in energy efficiency);
an estimation for the transmission cost, indirectly linked to SDG7.1 (by 2030, ensure universal access to affordable, reliable and modern energy services); and estimates for the social and environmental impacts, linked to multiple sub-objectives of SDG15. The existing literature uses a variety of criteria as an assessment of these terms. For this particular study, we take the factors that are relevant to the study area and more commonly used in the existing literature, although the exact definition of each factor may vary between the different studies.

The following list enumerates the layers considered for the MCDA, the SDGs with which they are directly or indirectly related, and some instances of their application in the existing literature:

* Distance to the electric grid (SDG7, as in [61–64])

* Distance to the road network (SDG7, as in [50,65–67])

* Distance to population nuclei (over 100 inhabitants) (SDG7, as in [68–71])

* Slope (SDG7, SDG15; as in [52,58,60,72])

* Land use (SDG2, SDG15, following [56], but also as in [51,54,57, 62])

Each of these GIS layers takes integer values between 1 and 5, both included, with values increasing with suitability. In Appendix B, we provide a specific description and the criteria used for value assignation for each of these layers.

In order to obtain a unique suitability characterization for each climatic grid box, we first need to find a unique value of suitability for each 100-meter pixel. This suitability value represents how good a pixel is for installation when considering all the layers mentioned. Since different factors may not affect the overall suitability in the same way, we assign a different weighing factor to each layer.

The most common method to assign the values of these pondering factors is some form of subjective weighting method [73]. However, studies in the literature are not consistent in terms of the relative importance of factors (see Table B.4 for an inter-comparison of different studies). Given this variability in the assignation of the weights, we take as reference those proposed in [59] because of the geographical location considered (contained within the area presented in this study) and the use of all the factors included in this study except for the land use. We assume a weight of land use of 20%, and accordingly adjust the values from the reference study to take up a total weight of 80%.

### 3.1.3. Parameterization of suitability cost

The final step to the incorporation of suitability to the optimization is to transform it into a cost. By construction, suitability can only take values between 1 and 5, with 5 representing the most suitable areas and 1 representing the least suitable ones. Given the limits of suitability, we propose a transformation to assign costs (going from zero to one) to all pixels, namely

$$s_k = 1 - \frac{S_k - 1}{5 - 1}, \quad (5)$$

with $S_k$ the suitability index for a given 100-meter pixel and $s_k$ the associated pixel suitability cost, both dimensionless. More specifically, $s_k$ represents the normalized values that regulate the suitability cost. An additional parameter is necessary in order to scale this magnitude to realistic values, and it is this parameter that characterizes the importance given to suitability in the optimization.

One additional step is required to convert the costs of suitability of the pixels inside a climatic grid box to a cost associated to the climatic box itself. We assume an optimal deployment of installations within each grid box, in which a merit-order effect is followed: capacity is first located in the pixel with the lowest suitability cost, then the second lowest suitability cost, and so on. This generates a distribution of the pixel suitability costs within individual grid boxes (Fig. 2). A third order polynomial is found to be the function that best fits these distributions, with all $R^2$ values exceeding 0.99. The suitability cost of a grid box installed capacity is the sum of all individual pixel installations; therefore,

the functions that describe the grid box suitability cost are the integrals of the fitted functions: fourth order polynomials. These integrals do not present an independent term as, by definition, the cost of not installing any capacity is zero.

## 3.2. Formulation of the optimization problem

In order to formulate a complete optimization problem, we take the system total cost function presented at the start of Section 3, and add a term representative of the suitability cost as described in Section 3.1.3. The new expression for the system total cost becomes

$$STC_{a,\gamma} = T_0 \sum_i x_i hRC_i + \alpha \sum_i q^2(t) + \gamma T_0 \sum_i a_i \Delta x_i^4 + b_i \Delta x_i^3 + c_i \Delta x_i^2 + d_i \Delta x_i, \quad (6)$$

with the two first terms the same as in Eq. (1), and the third term the cost of suitability of renewable energy capacity. $a_i$, $b_i$, $c_i$, and $d_i$ are the coefficients for the suitability quartics for each technology and grid box $i$ (in $\mathbb{E}$), and $\Delta x_i$ is the additional installed capacity over the 2020 scenario (see Fig. 3 for a reference on its spatial distribution). The parameter $\gamma$ is a non-negative coefficient that scales the cost of suitability in relation to the other terms forming the STC. For further reference, the three terms are named the VRE installation cost, the dispatchable generation cost, and the VRE suitability cost, respectively.

We introduce two additional modifications to the original STC optimization problem as presented in Eq. (4). The lower limit to the installed capacity is changed from zero to the installed capacity at the end of the reference year 2020 (Fig. 1 top). The upper limit to the installed capacity is converted to a limit on the total available area ($A_r$, with $r$ the index for each region/climatic grid box and $p$ the number of technologies), so that for each climatic grid box the total surface occupied by both technologies is limited instead of the capacity for each of them.

Therefore, the optimization problem is reformulated as

$$\begin{array}{ll} \displaystyle \min_x \mathbb{E}(S\bar{T}C(x)) & \\ \text{s.t. } x_i^{\min} \le x_i, \quad i \in 0, \dots, m-1 & (7) \\ \text{and } \sum_p \frac{1}{\rho_p} x_{r,p} \le A_r, \quad r \in 0, \dots, \frac{m}{p}-1, & \\ \text{with } \frac{1}{\rho_p} = 0.2 \text{ km}^2/\text{MW for wind, and } \frac{1}{\rho_p} = 0.02 \text{ km}^2/\text{MW for PV.} & \end{array}$$

## 3.3. Data

We use the ERA5 reanalysis [74] as the climate data source, Red Eléctrica de España as the electricity and market price data source, and the Spanish Ministry for the Ecological Transition and the Demographic Challenge as the installed capacity source. The main data source for the different layers of suitability is the Spanish Instituto Geográfico Nacional de España (IGN). Excluding the natural protected spaces (that combine data from IGN and the Spanish Ministry for the Ecological Transition and the Demographic Challenge) and land use (CORINE Land Cover is derived from the homonymous European project, although this data is made available through IGN), all other suitability data has IGN as its original source.

We conduct this analysis using hourly data for a 5-year period comprising the years 2016–2020, both included. We use the ERA5 variables for wind at 100 m, temperature at 2 m, and surface shortwave downward radiation at surface. Wind energy generation is estimated from wind, and PV generation is calculated from radiation and temperature (which affects the efficiency), and both are translated to the corresponding capacity factors and calibrated using the observed REE electricity data on both generation sources. Observed hourly demand is used to fit a temperature-dependent function that relates demand to its base component and some additional terms related to heating and cooling systems.
<figure><img src="image_10.png" /><figcaption>Fig. 2. Distribution of suitability costs with the percentage of occupation of each grid box (thin gray lines) for wind (left) and PV (right). The thick black line represents the mean. The top left corner of each panel shows the coefficient of determination ($R^2$) value of the third order polynomial fit of the mean.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 3. Pseudo cost of suitability (Eq. (6)) for $\Delta x_i$ of 10 MW (top), 100 MW (middle) and 1000 MW (bottom) for PV (left) and wind (right). Notice the logarithmic scale in the middle right and bottom left panels. Black crosses mark points where capacity of a given technology exceeds the maximum occupiable surface.</figcaption></figure>

In addition to the calibration process, REE data is also used to estimate the $\alpha$ coefficient under the assumption of a perfect market, using the relation of generation cost and market price and dispatchable generation. IGN data is used to estimate both the area available for

installation and its suitability. Given that the ERA5 resolution over Spain is around 20 km, grid boxes typically include around 40000 pixels, although this number is reduced for grid boxes near the Spanish borders whether with other countries or the sea. The number of pixels
<figure><img src="image_12.png" /><figcaption>Fig. 4. Characterization of reference values of the 2020 capacity distribution for α (left) and γ (right). On the left, points represent daily data for total market price and daily dispatchable generation for the 2016–2020 (blue) and 2021–2022 (orange) periods, and the black line represents the ordinary least squares regression for the 2016–2020 data (95% confidence interval shadowed in gray). Dashed lines indicate the slope associated to the annotated α value. The determined α<sub>REF</sub> and coefficient of determination are shown. On the right, the root mean square difference (in MW) between the 2020 mix and each optimal repowering distribution is shown with γ.</figcaption></figure>

used in the calculation of the suitability coefficients is then reduced
considerably if many pixels inside it are deemed uninstallable.

3.4. Characterization of dispatchable energy cost

As a mean to contextualize any further results, we first aim to
characterize the parameters (α and γ) that drove the system towards
the 2020 mix. The parameter α determines the relationship between
the dispatchable energy generated and the variable cost associated to
it, and consequently relates the dispatchable generation needed for the
system and the final market price of energy. In more mathematical
terms, it characterizes the specific shape of the quadratic term in
Eq. (6), determining the growth rate of energy costs with dispatchable
generation. In this study, we work under the assumption of a perfect
market [75], and take an empirical approach to estimate this factor
using the real market price. Since we work under the assumption
that the total cost of dispatchable generation takes a quadratic form,
the market price of energy (λ) can be estimated as λ = 2αq. This
market price information combined with the dispatchable generation
data helps estimate the characteristics of the existing α values as well
as possible existing trends.

REE has data for the daily mean market price, and the hourly total dispatchable generation, which can be aggregated into the corresponding daily totals. For each daily price-generation pair between 2016 and 2022 we can identify a value of α (Fig. 4 left). We differentiate the 2016–2020 data from the 2021–2022 information, as only the first period contributed towards the creation of the existing mix. Similarly, for the 2016–2020 period we identify a global value of α descriptive of the overall period.

The parameter α shows two clearly differentiated behaviors. In the
years between 2016 and 2020, no values exceed the 2 · 10⁻³€/MWh².
Considering an overall α for the 2016–2020 period yields a value of
1.25 · 10⁻³€/MWh² (α<sub>REF</sub> from this point onward). Contrarily, the days
in 2021 and 2022 present values mostly comprised between 4 · 10⁻³
and 9 · 10⁻³, with a lot of variability and very little overlap with the
individual values comprising α<sub>REF</sub>. This illustrates a change in the
regime that regulates the price. Therefore, installations made before
2020 have been made under the regime dominated by α<sub>REF</sub>, but
the future deployment of VRE sources will operate under a system
characterized by higher α values.

3.5. Characterization of the current trade-off between renewable penetra-
tion and suitability for installation

In order to complete the characterization of the 2020 mix we estimate its associated $\gamma$ parameter. To do so, we assume that the model is sufficiently representative of reality and explore the optimal repowering scenarios (i.e. as in Section 3.2 but exploring scenarios of capacity redistribution that keep the PV and wind total capacities unchanged). This repowering represents the optimal scenarios of VRE capacity that would have been realized if the best scenarios were consistently applied from the very initial installation. Even though repowering is unrealistic, this academic experiment helps estimate the $\gamma$ value that was implicitly used in the unfolding of the existing system by finding which of the optimal repowering scenarios better matches the actual 2020 mix.

These optimizations are performed for each value of $\gamma$ between
$5 \cdot 10^{-2}$ and $10^3$, covering the 1 and 5 values for each order of magnitude,
and using the $\alpha_{REF}$ obtained in Section 3.4 as seen in Fig. 4 left.
The resulting capacity distributions are then compared to the exist-
ing 2020 mix. By comparing these distributions, we are making two
implicit assumptions: the land suitability is unaltered with renewable
installations, and the current distribution is close to optimal. Under this
framework, it is possible to analyze how the different $\gamma$ values change
the distribution of the installed capacity.

In order to determine an approximation to the current $\gamma$, we use
the root mean square difference (RMSD) as a measure of the similarity
between a given optimal repowering capacity distribution and the
existing mix. Ideally, we would identify as the closest mix the one with
the RMSD closest to zero. In this analysis (Fig. 4 right), the value of
$\gamma = 10$ presents the lowest RMSD. This value ($\gamma_{REF}$) is used as reference
for the analysis of experiments with varying values of $\gamma$ representative
of changes in socio-environmental awareness.

4. Land-energy trade-off: impacts on the energy mix

In this section, we explore the optimal renewable energy deploy-
ment scenarios, describe the results obtained within the e4clim frame-
work, and discuss their extrapolation to real-world applications.

4.1. Sensitivity of the system to changes in the suitability coefficient

In addition to the estimation of $\gamma_{REF}$ done in Section 3.5, we
explore the impacts on VRE deployment scenarios (e.g., penetration
and STC) produced by changes in the values of $\gamma$. Results show three
<figure><img src="image_13.png" /><figcaption>**Fig. 5.** Evolution of mean penetration (in %, top) and system total cost (in G€, bottom) with $\gamma$ (log scale, left) for each $\alpha$ and $\alpha$ (right) for each $\gamma$. Vertical dotted lines represent the estimated values for $\gamma_{REF}$ (left) and $\alpha_{REF}$ (right). In the top panels, dashed horizontal lines represent the 2030 (gray) and 2050 (black) penetration objectives established at the Spanish level.</figcaption></figure>

different regimes (Fig. 5 left). Considering values of $\gamma_0 = 10^{-1}$ or lower does not impact the mean penetration of VRE sources or the STC, implying that it is practically equivalent to not including the suitability term altogether, and only changing by means of changes in $\alpha$, following the original formulation of the optimization problem described in Eq. (4). This case describes a scenario where $\gamma$ is practically zero, and therefore the only objective in terms of VRE is to reach the highest possible penetration. Values of $\gamma_\infty = 10^3$ or higher yield the penetration fixed by the minimum installed capacity independently of the cost of dispatchable sources, implying that the cost of suitability becomes so large that any renewable installation is considered too costly for the system. As another consequence, the STC is almost fixed for each $\alpha$ at large $\gamma$ values, only changing because of the increase in the cost of the dispatchable generation by construction, which has to cover all the demand not covered by the minimum capacity. Finally, we identify a transition regime between the two extremes, where even slight modifications to $\gamma$ provoke large changes to the VRE penetration and the STC, and with $\gamma_T = 10$ (T for transition) the intermediate value that matches $\gamma_{REF}$.

This analysis of system sensitivity to $\gamma$ along with the overall exploration of $\alpha$ and $\gamma$ values constitutes an analysis of system sensitivities and uncertainties. However, additional sensitivities to system elements are present at multiple steps of the process. Appendix D presents a comprehensive exploration of the most relevant uncertainties in the modeling system, addressing them through bibliographical and experimental approaches.

## 4.2. Changes in system total cost and mean penetration

The selection of $\gamma$ limits both the penetration levels that can be reached, and the cost of dispatchable generation at which VRE installations become profitable (Fig. 5 right). As the cost of dispatchable generation increases, so does the penetration of VRE sources, as they become more profitable in comparison to their dispatchable counterparts. The incorporation of VRE sources to the mix has a double impact on the STC: it increases the STC in terms of VRE installation and suitability costs, but diminishes the presence of dispatchable sources in the mix, and consequently reduces the cost of dispatchable generation. It is this trade-off that sets the dispatchable generation cost (determined by $\alpha$) at which the installation of VRE becomes profitable in terms of STC.

For $\gamma_\infty$, the most important consideration to prevent STC growth is to keep the VRE suitability cost low. Therefore, penetration increases very slowly, as the high suitability cost makes additional VRE not profitable. This lack of additional VRE capacity translates into a linear evolution of STC with dispatchable generation cost, since it becomes the dominant term and increases linearly with $\alpha$. This behavior is clearly depicted in the decomposition of STC into its components (Fig. 6 bottom), which confirms the dominance of the dispatchable generation term and its linear dependence on $\alpha$.

The opposite case is represented by $\gamma_0$, which gives little importance to the suitability term. Under this regime, penetration increases very rapidly with the cost of dispatchable generation. This is caused by VRE sources with very small suitability costs becoming more profitable
<figure><img src="image_14.png" /><figcaption>**Fig. 6.** Evolution of the decomposition of system total cost (G∈) with α for γ of 10⁻¹ (top left), 10 (top right) and 10³ (bottom). The decomposition shows the terms described in Eq. (6): dispatchable generation cost (blue), the VRE installation cost (orange), and the VRE suitability cost (green). The vertical dotted line indicates the characterized α<sub>REF</sub> value.</figcaption></figure>

than dispatchable ones with small α increments. As a consequence, penetration increases rapidly with α, but STC grows at low rates. The installation of VRE sources if additional suitability cost is small is always a favorable option when the cost of dispatchable energy increases, both in terms of greater coverage of the demand by renewable generation and cheaper STC. The decomposition of STC (Fig. 6 top left) clearly depicts the dispatchable cost stalling at quite low values of α. The amount of dispatchable generation needed is reduced as a response to the introduction of VRE, compensating for the increasing value of α and reaching a stable balance for the dispatchable cost.

In the intermediate case represented by $\gamma_T$, a behavior similar to $\gamma_0$ occurs but the big leap on the presence of VRE is delayed to higher $\alpha$ values, and the change in growth is slightly slower. The individual terms of its STC decomposition (Fig. 6 top right) show an intermediate behavior as well. The suitability cost of VRE hinders the introduction of VRE. In similarity to the $\gamma_0$ case, the dispatchable energy cost slows its growth (although not completely stalling in this case) by effect of the increasing penetration.

Despite having a small final contribution, the sensitivity of the optimization to VRE suitability is very high, and its cost strongly influences the optimal distributions of capacity (as will clearly be seen in Section 4.3). A clear example of this is that $\gamma_0$ and $\gamma_\infty$ both have a very small suitability term but with rather different reasons behind. For $\gamma_0$, the importance given to the suitability cost is so small that the cost associated to it is correspondingly small. Comparatively, for $\gamma_\infty$, the suitability is effectively considered as the most important factor whose cost should be reduced, making even little concessions in terms of suitability expensive. This translates to these concessions only being made in small amounts when dispatchable cost becomes so large that the suitability cost is preferable.

Some real-world implications can be extracted as an extrapolation of these results, keeping in mind that increments in $\gamma$ represent incremental awareness of socio-environmental and technical aptness. Certain levels of penetration are unreachable when $\gamma$ is high (Fig. 5

left), meaning that if some compromises are not made in terms of the suitability of installations some objectives may not be met. For instance, the 42% penetration objective established for 2030 at the Spanish level is not attainable for $\gamma_\infty$, which highlights the need for these concessions. Similarly, the 80% target for 2050 barely becomes a profitable optimal mix with $\gamma_T$ if dispatchable generation becomes very expensive, but is otherwise unreachable. In order to meet these highly ambitious objectives, strong adjustments will have to be made in terms of suitability, and some less than ideal areas will necessarily be used for VRE installation. One of the possible solutions is for offshore technology to gain relevance, although it would raise different concerns, particularly in the Spanish case which seems to be particularly tough for this type of development due to both coastal features and social aversion [76].

### 4.3. Optimal capacity distribution for different trade-off scenarios

The penetration and STC evolution curves directly stem from the optimal distributions of VRE installed capacity. To better understand the effect of $\gamma$ on the allocation of capacity, we analyze the spatial distribution for $\gamma_0$, $\gamma_\infty$, and $\gamma_T$ for a fixed value of $\alpha = 3 \cdot 10^{-3}$, a small increment with respect to $\alpha_{REF}$. It should be noted that these capacities represent additions to the 2020 mix, and not the full capacity distribution. We select this increased value with respect to the $\alpha_{REF}$, as it reproduces the increments of varying amplitudes seen in the most recent years, and depicts them as a slightly higher general fixed $\alpha$ value, assuming a period with stable slightly higher prices. It is important to note that by fixing $\alpha$, our analysis on different $\gamma$ values implies that capacity distributions do not reach the same levels of penetration, but respond to scenarios with equivalent variable cost functions for dispatchable generation.

The capacity distribution generated by $\gamma_0$ (Fig. 7 top) is dominated by PV installations at the south and east of the Spanish territory, combined with the installation of wind technology at the points with
the largest influence from Atlantic winds, located at the southwest and southeast of the domain. The mix is completed by other high-capacity wind installations in the central part of Spain, as well as some northern PV installations. These installations are located at the areas with the highest climatic resource, in some cases even occupying the entire surface available for installation in a given grid box. This deployment is possible due to the small weight given to the suitability cost, as the installation penalty is very little. The result of this is a capacity distribution that reaches a mean penetration over 70%.

The other extreme case is $γ_∞$ (Fig. 7 bottom), which presents a very spread out distribution with lots of installations of little capacity. This is true for both wind and PV, although the higher density of installation achievable by PV allows for its individual installations to be larger. This distribution is dominated by the effect of the suitability cost. As a consequence of the convex suitability cost, additional units of VRE in a given location become more and more expensive, a phenomenon that is usually compensated by spreading or reducing installed capacity. The strong restrictions imposed by the suitability cost yield a mean penetration level barely exceeding the 30% mark, with very little increment with respect to the level reached by the 2020 installed capacity.

The moderately restrictive case represented by $γ_T$ (Fig. 7 middle) presents a very scattered distribution, with most of the capacity allocated in small installations. However, some locations presenting moderate-sized deployments (around 1 GW) remain in the mix. Most wind capacity installations, and especially those with capacities around the 500 MW mark, are located in regions similar to those in the $γ_0$ mix. The same is true for the PV distribution, which presents capacity allocated in the same locations of the $γ_0$ mix, with some additional locations especially in the western side of the domain, which had no capacity allocated when suitability was not a relevant factor. This moderate weight associated to the suitability cost introduces some restrictions to the installation size, but maintains a preference for the high-resource locations examined in the $γ_0$ mix. This balance between the VRE penetration and suitability manages to attain around 55% mean penetration.

The translation of these results into real-world projections seems to show a clear tendency: as the social awareness to protect the environment and find cheaper technical solutions (i.e., $γ$) increases, the optimal mixes become increasingly scattered, with overall lower capacities at individual locations. Given a fixed location, the suitability cost of each additional unit is higher than the previous one if they are being optimally deployed. This implies that given two identical locations for installation, splitting the installation between the two is cheaper overall. Therefore, as the suitability term gains importance, it becomes more and more beneficial in terms of system total cost to spread out the installations. This scattering of installations comes at the expense of generally lower penetrations, since the areas with the most climatic resource become too expensive in terms of suitability when the capacity they accommodate increases. Any cost consideration in terms of suitability yields a reduction in the coverage of demand by VRE sources in the interest of lowering the impact of new capacity on socio-environmental and economic terms.

## 5. Land-energy trade-off: socio-environmental impacts and link to existing development plans

The spatial distribution of optimal energy mixes indirectly shows the occupation of land, but it does not give any information on their specific impacts on sustainability. Therefore, to obtain a wide vision of the effect of renewable energy installations, we conduct a global analysis using relevant SDGs as proxy.

### 5.1. Relation of optimization terms to sustainable development goals

The potential relations between the SDG indicators and optimization terms, including suitability terms, are made explicit in this section. Indicators are worded exactly as in the SDGs of the United Nations [48]. Relevant indicators are presented in Table 1 with the correspondence to the optimization or suitability terms.

Note that the selected indicators represent a selection of the 42 indicators contained in 30 targets that are relevant to the four presented SDGs. The selection of these indicators refers to the most relevant features in the context of our assessment of VRE generation and the effect of its deployment on land. Nevertheless, other applications of similar methodologies may require the use of different indicators in order to better reflect the trade-offs between the system elements, sometimes even requiring the design of indicators not included in the formulation of the SDGs. In this work we limit our analysis to the official UN SDG-derived indicators and targets.

To analyze these indicators as a whole instead of in isolation from one another, we turn to the spider diagram that identifies how each optimal mix links to the SDG indicators, and allows for a simultaneous assessment of all relevant terms [77]. The explicit process through which optimization-derived results are transformed to the indices associated to these indicators are made explicit in Appendix C.

The fulfillment of the indicators by the three scenarios of interest (Fig. 8) shows some striking patterns. First, none of the three considered scenarios present particular ambition towards the objectives associated to the SDG7. That is, these three scenarios present moderate to low achievement of the energy-related goals. This result was to be expected, as the indices have been determined using optimal mixes considering up to triple the value of $α$. Nevertheless, these patterns reflect the ones already discussed in Section 4.

The $γ_0$ scenario, more ambitious on the SDG7 indicators, also presents the most favorable scenario in terms of emissions (SDG 13). However, it implies the need to make moderate compromises in terms of SDG2 and SDG15. The opposite is true for the $γ_∞$ scenario, which minimally contributes towards SDG7 and SDG13 indicators, but presents very strong territorial protection in the form of SDG2 and SDG15. In the middle of these two scenarios, and considering the area inside the curve in Fig. 8 as a proxy for the overall alignment with the SDGs, the $γ_T$ scenario presents itself as the best global option.

These three scenarios depict the trade-offs that are central to this article. When energy-related objectives are prioritized (SDG7, SDG13), the compromises necessary in terms of land increase (SDG2, SDG15). This implies that energy-related SDGs directly conflict with land-related ones. However, the existence of a scenario that manages to reach limited sacrifices (never more than a unit in index terms) in all SDGs with respect to the best of the presented scenarios introduces an optimistic scenario towards future deployments, which in our case is marked by $γ_{REF}$.

In an additional characterization of these three mixes under the nexus approach, we can analyze the silo indices for each of the four involved SDGs. In the case of SDGs 2 and 13, their silo indices are directly the corresponding spider diagram indices. For SDG 15, its silo index is the average of its two spider diagram indices. Finally, for SDG 7 it is a weighted average of its three spider diagrams, as $7.b.1*$ is given a half the weight of the other two since it is not directly applicable to the Spanish case (i.e., weights of 0.4 to 7.1.2 and 7.2.1, and 0.2 to 7.b.1*). The resulting nexus index is the average of the four individual silo indices. The resulting values for the three analyzed mixes are shown in Table 2.

The quantification of the nexus index for the three scenarios confirms the conclusions obtained from a visual analysis of Fig. 8. The $γ_T$ mix, which stood out as covering the largest area in the spider diagram, stands out as the one with the highest nexus index. Despite not presenting the highest standalone silo index in any case, a global vision clearly identifies this mix as the best nexus selection. This emphasizes the need for a nexus approach, as narrowly focused sustainable development objectives may hide damaging effect to other relevant sustainability issues.
<figure><img src="image_15.png" /><figcaption>Fig. 7. Distribution of optimal capacities for PV (left) and wind (right) for $\gamma \ 10^{-1}$ (top), 10 (middle), and $10^3$ (bottom) for $\alpha = 3 \cdot 10^{-3}$. Installations under 1 MW are represented by small white circles. Locations where the maximum available surface is occupied present a black border on the corresponding circles.</figcaption></figure>

## 5.2. Characterization of stakeholder plans and comparison to optimal deployment scenarios

The results presented in this article up until this point show the optimal VRE deployment for the near future in Spain in the context of the e4clim model. In order to give context to the discussion, we analyze the similarity between these results and real-world plans by comparing them to the existing plan for the development of the Spanish electricity system 2021–2026 [42], which includes information on the planned VRE development in this 5-year period. This plan accounts for the installation of around 19 GW of PV and 18 GW of wind. Since the plan has quantitative information at the autonomous community level, we regroup our optimization points and analyze them at this

spatial division. The comparison of the optimal deployment scenarios and the plan can help estimate the compromise that is being made in terms of renewable penetration, and socio-environmental awareness and technical aptness under the assumption that these plans are optimal.

The existing deployment plans (Fig. 1 bottom) set to install most PV capacity in the southernmost part of Spain, with most complementary capacity in the central regions. Other regions contain lower individual capacities, which combined with the rest amount to the total capacity to be installed. The wind plan is complementary, with the majority of the capacity appointed to be installed in northern areas, but complementary smaller installations spread out all along the territory.
<caption>**Table 1**</caption>

Sustainable Development Goals and their indicators related to the present study. The characterization column briefly indicates the relation used to translate the results to indices related to the indicators. The sign reflects the relation between the characterization and the indicator: + for an increasing value favoring the indicator, - for a decreasing value favoring the indicator. For further development, refer to 5.1.

<table><thead><tr><th>SDG</th><th>Indicator</th><th>Characterization</th><th>Sign</th></tr></thead><tbody><tr><td>2 Zero hunger</td><td>2.4.1 Proportion of agricultural area under productive and sustainable agriculture</td><td>Occupied land with CLC 1 or 2</td><td>-</td></tr><tr><td rowspan="3">7 Affordable and clean energy</td><td>7.1.2 Proportion of population with primary reliance on clean fuels and technology</td><td>Sum of distance to urban nuclei index over all occupied land</td><td>+</td></tr><tr><td>7.2.1 Renewable energy share in the total final energy consumption</td><td>Mean penetration</td><td>+</td></tr><tr><td>7.b.1* Installed renewable energy-generating capacity in developing countries (in watts per capita)</td><td>Watts of installed capacity per capita</td><td>+</td></tr><tr><td>13 Climate action</td><td>13.2.2 Total greenhouse gas emissions per year</td><td>Total emissions in tons of CO2 equivalent</td><td>-</td></tr><tr><td rowspan="2">15 Life on land</td><td>15.1.1 Forest area as a proportion of total land area</td><td>Occupied land with CLC 3</td><td>-</td></tr><tr><td>15.3.1 Proportion of land that is degraded over total land area</td><td>Total area occupied by installations</td><td>-</td></tr></tbody></table>

<figure><img src="image_16.png" /><figcaption>**Fig. 8.** Level of accomplishment of each Sustainable Development Goal indicator for $\alpha = 3 \cdot 10^{-3}$ and $\gamma_0$ (blue), $\gamma_T$ (orange), and $\gamma_\infty$ (green). Large values of indices along the axes indicate higher fulfillment of the indicators.</figcaption></figure>

<caption>**Table 2**</caption>

Quantification of the silo indices for food (2), energy (7), climate (13) and land (15) Sustainable Development Goals, as well as the nexus index for the three mixes of interest.

<table><thead><tr><th>Scenario</th><th>SDG 2</th><th>SDG 7</th><th>SDG 13</th><th>SDG 15</th><th>Nexus index</th></tr></thead><tbody><tr><td>γ<sub>0</sub></td><td>3</td><td>3</td><td>5</td><td>2.5</td><td>3.375</td></tr><tr><td>γ<sub>T</sub></td><td>5</td><td>2.2</td><td>4</td><td>4.5</td><td>3.925</td></tr><tr><td>γ<sub>∞</sub></td><td>5</td><td>1</td><td>1</td><td>5</td><td>3</td></tr></tbody></table>

We will consider this planned deployment as the reference to compare to our optimal mixes. Since the actual value of $\alpha$ for upcoming years remains unknown, and the $\gamma$ determining the suitability-associated costs cannot be precisely determined, we take the penetration as the reference to select the mixes to compare to the plan. Adding the existing plans to the existing capacity at the end of 2020 produces a mean penetration of approximately 50%. Therefore, we analyze the combinations of $\alpha$ and $\gamma$ (observable in Fig. 5 top, and hereby assigned a name) that return penetrations around this value: $\alpha = 2 \cdot 10^{-3}$, $\gamma = 1$ ($\gamma_0^P$); $\alpha = 3 \cdot 10^{-3}$, $\gamma = 10$ ($\gamma_T^P$); $\alpha = 7 \cdot 10^{-3}$, $\gamma = 100$ ($\gamma_\infty^P$). We do not
<figure><img src="image_17.png" /><figcaption>**Fig. 9.** Replication of the capacity deployment from the Spanish development plan (Fig. 1 bottom) with data from optimal mixes with 50% penetration. Corresponding $\alpha$ and $\gamma$ values, and the root mean square difference with respect to the actually planned capacity are annotated.</figcaption></figure>

explicitly analyze $\gamma = 0.1$ because it is practically equivalent to $\gamma = 1$, and do not analyze $\gamma = 50$ in favor of $\gamma = 100$. Additionally, we do not analyze $\gamma = 500$ or $\gamma = 1000$ because they do not meet the 50% penetration level.

A first analysis based on RMSD (similar to the one used for the estimation of $\gamma_{REF}$ in Section 3.5) shows that, if the existing plan is optimal, it is aligned with the level of compromise marked by $\gamma_{REF}$. Focusing on the specifics of the spatial distributions, firstly for $\gamma_0^P$ (Fig. 9 top), most of the capacity turns to the most resourceful areas: PV towards the south, wind towards the northwest. This creates quite uneven distributions, especially in the case of PV, producing heterogeneity that may lead to difficulties in terms of the distribution and transmission networks, factors that are not considered in our model.

In the case of $\gamma_\infty^P$ (Fig. 9 bottom), most of the capacity is allocated in the same region for both PV and wind. This region is the largest

one in the domain, having the largest availability for installation, and presenting generally low suitability costs even for large capacities (as seen in Fig. 3). The rest of capacity is quite spread out, especially in the case of wind. The importance given to the suitability cost returns distributions that no longer focus on utilizing the high resource areas, and that require larger installations in substandard (in terms of climatic resource) regions to reach equivalent levels of penetration.

The capacity distribution for $\gamma_T^P$ (Fig. 9 center) returns mixes with some similarities to the ones depicted in the development plan (Fig. 1 bottom). The majority of the PV capacity is located in the southern and westernmost regions, whereas the wind capacity is located in the northernmost areas. Areas with over 10% of capacity present qualitative resemblance with the plan. Therefore, the analysis of the spatial deployment suggests that the current development plan for the Spanish electricity system follows a moderate $\gamma$, maintaining the
compromise made with $γ_{REF}$ to reach the current mix. The proposed installations manage to appeal to the delicate balance between meeting the established energy-related goals and maintaining land preservation concessions, following the optimal patterns for the overall fulfillment of SDGs.

## 6. Conclusions

The social compromise towards the integration of increasingly more VRE sources in the coming years is made clear by the strong implication of institutions at all levels; a combined effort that could allow future installations to take the most advantage of the climatic resource and its synergies. However, during this transition it is fundamental to keep in mind that energy and electricity only represent a specific part of societal needs, which should not irreversibly curb the possibility of covering others such as food production or landscape preservation. The strong impacts of VRE deployment on land make the consideration of the nexus between land and energy imperative.

In this study, the elements related to the VRE installation allocation and use of terrain were combined into a single magnitude that allows for a wider vision of the electricity system: the cost of suitability. Under the minimization of STC, we have analyzed changes to the optimal mixes under the modification of suitability cost. When prioritizing VRE penetration, capacity focuses on high-climatic-resource points, while emphasizing suitability spreads capacity out. Very strong considerations of suitability allow barely any additional capacity to be installed, not exceeding the 35% penetration mark, therefore not reaching future objectives. VRE deployment is highly sensitive to suitability costs, despite comprising under 15% of STC. In fact, mean renewable penetration increases with suitability permissiveness, reaching increments up to 70%.

The decision on the weight given to suitability-related costs is a compromise, signifying the balance in the land-energy nexus. Analyzing optimal mixes with the Spanish development plan shows the current approach balances penetration goals with installation suitability and land preservation. This mirrors the 2020 mix, which best fulfills SDGs in terms of clean energy, climate action, food production, and land preservation. This approach could meet 2050 objectives of 80% renewable penetration, with a 20% cost increase compared to a more permissive option, but still half the cost of a more restrictive land protection policy. Finding the right balance between energy and preservation efforts is subjective, but short-term economic investments in both fronts can prevent long-term adverse situations and support overall SDGs. In fact, taking the right approach can increase the contribution to SDG fulfillment between 15 and 30%.

Unpopular decisions may be necessary to meet future penetration targets, but careful location selection and sufficient investment can help maximize the benefits. VRE expansion is vital for emissions reduction, but preserving land services like ecosystems is equally crucial. Long-term energy security should not overshadow the needs of both humans and ecosystems. Energy sobriety, focusing on reduced energy consumption, is an effective strategy to minimize generation pool expansion. In any case, maintaining the balance between energy and other land services is essential. Our study underscores the importance of finding suitable land for VRE installations, emphasizing that sustainability goes beyond clean energy. Future developments should prioritize the harmonious consideration of climatic resources and land occupation at an equilibrium. They should also avoid highly localized exploitation of climatic resource an account for the social resistance to further expansions.

### CRediT authorship contribution statement

**Aina Maimó-Far:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Víctor Homar:** Writing – review & editing, Validation, Supervision, Software, Resources,

Project administration, Investigation, Funding acquisition. **Alexis Tan-tet:** Writing – review & editing, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Philippe Drobin-ski:** Writing – review & editing, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

Data will be made available on request.

### Acknowledgments

This research is framed within the TRAMPAS (PID2020-113036RB-I00/AEI/ 10.13039/501100011033) project funded by the Spanish Agencia Estatal de Investigación (AEI) from the Spanish Ministerio de Ciencia e Innovación. Author A. Maimó-Far received funding from the Spanish Ministerio de Ciencia Innovación y Universidades (FPU18/00520). This research made use of e4clim, an open source software, developed in the frame of the Energy4Climate Interdisciplinary Center (E4C) of Institut Polytechnique de Paris and École des Ponts Paris-Tech and supported by the 3rd Programme d'Investissements d'Avenir [ANR-18-EUR-0006-02] and by the Foundation of École Polytechnique (Chaire Défis Technologiques pour une Énergie Responsable). The authors would like to thank Joan Bauzà Llinàs and the Servei de SIG i Teledetecció de la Universitat de les Illes Balears for providing the geographical data.

## Appendix A. Estimation of capacity density

In order to make use of all this land availability and suitability information, we need to know (or at least approximate) how much land each renewable installation takes up, and for this estimate, we turn to the existing literature (see Table A.3 for an overall summary). The National Renewable Energy Laboratory [78] of the United States performed these estimations through analyzing existing literature, their own database of existing systems, and the contributions of interviewed NREL experts. The resulting estimates reported values for PV installations of 0.013, 0.022 and 0.025 km²/MW and for wind installations of 30.121 and 0.181 km²/MW.

In a recent study for wind [79] performed an explicit analysis of existing farms and some literature review and obtained a mean of 0.051 km²/MW for the observed plants, although observed values from previous studies ranged from 0.074 to 0.345 km²/MW. The 17 onshore wind farms observed with the corresponding installed capacity and occupied space (containing a wide variety in the number of turbines, between 7 and 131) per farm ranged from 0.021 to 0.161 km²/MW.

The data collected by the Danish Energy Agency [80], although not directly addressing the space occupied by technology, provides some

<table><caption>Table A.3
Land necessary for the installation of technology, in km²/MW.</caption><thead><tr><th></th><th>Wind</th><th>PV</th></tr></thead><tbody><tr><td>[78]</td><td>0.121-0.181</td><td>0.013-0.025</td></tr><tr><td>[79]</td><td>0.021-0.161</td><td>-</td></tr><tr><td>[80]</td><td>0.32-0.57</td><td>0.011-0.013</td></tr><tr><td>[81]</td><td>0.088</td><td>0.012</td></tr><tr><td>[82]</td><td>0.2</td><td>0.018</td></tr><tr><td>[83]</td><td>0.12</td><td>0.017-0.02</td></tr><tr><td>[84]</td><td>0.125-0.189</td><td>0.014</td></tr><tr><td>This study</td><td>0.2</td><td>0.02</td></tr></tbody></table>
<caption>Table B.4</caption>

Weights attributed to distance to urban areas, distance to the electricity grid, distance to roads, slope and land use in different studies. Weights do not necessarily add to 100% or 1, as some of the studies considered additional factors.

<table><thead><tr><th></th><th></th><th>Urban</th><th>E. grid</th><th>Roads</th><th>Slope</th><th>Land use</th></tr></thead><tbody><tr><td>[58]</td><td>Wind</td><td>18.5%</td><td>8%</td><td>7.4%</td><td>4.6%</td><td>6%</td></tr><tr><td>[71]</td><td>PV</td><td>0.21</td><td>0.11</td><td>0.10</td><td>0.03</td><td>-</td></tr><tr><td rowspan="2">[57]</td><td>Wind</td><td>0.0539</td><td>0.0772</td><td>0.0257</td><td>0.0297</td><td>-</td></tr><tr><td>PV</td><td>0.0201</td><td>0.0859</td><td>0.0286</td><td>0.0532</td><td>-</td></tr><tr><td>[49]</td><td>PV</td><td>1%</td><td>2%</td><td>2%</td><td>9%</td><td>5%</td></tr><tr><td>[59]</td><td>Wind +PV</td><td>0.0648</td><td>0.4281</td><td>0.1110</td><td>0.3959</td><td>-</td></tr><tr><td rowspan="2">[67]</td><td>Wind</td><td>0.059</td><td>0.106</td><td>0.086</td><td>0.094</td><td>0.084</td></tr><tr><td>PV</td><td>0.059</td><td>0.106</td><td>0.086</td><td>0.076</td><td>0.084</td></tr><tr><td colspan="2">This work</td><td>0.05184</td><td>0.34248</td><td>0.08896</td><td>0.31672</td><td>0.20000</td></tr></tbody></table>

useful estimates. For PV, between 0.011 and 0.013 $km^2/MW_p$, which directly converts to $km^2/MW$ if we assume that the peak generation corresponds to the installed capacity producing with a capacity factor of one. For wind, assuming a capacity of 3.5 MW, two different assessments of the affected area are considered: an affected area of 50 m × 50 m by design, or the noise-affected area with a range for the radius of 600 to 800 m. In real applications, the closest estimation to reality is considering the noise-affected area, although in the case of farms turbines can be closer together. This would yield an approximation for wind of 0.32 to 0.57 $km^2/MW$.

In a review of some major energy-related solutions that have been proposed, [81] sees that for a turbine with a rotor diameter of 126 m and a 5 MW capacity, a space of around 0.44 $km^2$ is necessary. This gives an approximate value of 0.088 $km^2/MW$. Similarly, for PV around 1.2 $km^2$ are required for the installation of 100 MW, resulting in a value of 0.012 $km^2/MW$.

In a very recent study, [82] made some approximations to the already-mentioned estimations from [79] for wind. Adding a disturbed area factor, an area of around 1 km by 1 km is assumed for a turbine of 5 MW, resulting in 0.2 $km^2/MW$. In the case of PV, the area occupied by each installation is smaller as not much spacing is required between panels. The approximate value proposed is 0.018 $km^2/MW$.

In France, both the electricity operator (Réseau de Transport d'Électricité, RTE [83]) and the French Environment and Energy Management Agency (Agence De l'Environnement et de la Maîtrise de l'Énergie, ADEME, [84]) have made some approximations to the land used by the installation of wind and PV farms. For RTE, considering the area affected by wind turbines produced a value of 0.12 $km^2/MW$, with the possibility of reaching values of 0.08 $km^2/MW$ in 2050. Similarly, for PV an estimated 0.017 to 0.02 $km^2/MW$ are reported, but with the projection of reaching 0.01 $km^2/MW$ by 2050. In the case of ADEME, the estimations made are between 0.189 and 0.125 $km^2/MW$ for wind and 0.014 $km^2/MW$ for PV.

## Appendix B. Construction of the suitability index

The suitability index is constructed from the layers mentioned in Section 3.1.2. Here we elaborate on the description of these layers and the values assigned to their classification. Unless specified otherwise, the classification is performed following natural groups [85].

### Distance to the electric grid

This layer represents the euclidean distance to the electricity grid, which is associated to increasing costs of building infrastructure. The lower the distance to the electric grid, the lower the cost of connecting the plant to the existing network and the higher the suitability.

### Distance to the road network

This layer represents the euclidean distance to the road network, which relates to the cost of construction and maintenance. The lower the distance to the road network, the lower the cost of construction and maintenance of the plant, and the higher the suitability.

### Distance to population nuclei (over 100 inhabitants)

This layer represents the euclidean distance to population nuclei with over 100 inhabitants, which relates to the cost of transmission and distribution. The lower the distance to the population nuclei, the lower the cost of transmitting the generation to the demand sites, and the higher the suitability. It is important to note that urban areas are deemed incompatible with the installation of renewable energy generation plants and are therefore excluded from consideration.

### Slope

This layer represents the slope of the terrain, which is associated to the cost of installation and maintenance. The criteria for assigning suitability values to slopes differs between technologies, as PV is generally more sensitive to steep slopes compared to wind. This difference creates a separation between the suitability indices of both technologies. To represent reality as precisely as possible, the relationship between slope and suitability is not assumed to be linear.

For PV, decreasing indexes are assigned to the intervals (with inclusive upper limits) as follows: under 1%, between 1% and 1.5%, between 1.5% and 2%, between 2% and 3%, and over 3%. Similarly, for wind the intervals are: under 10%, between 10% and 15%, between 15% and 20%, between 20% and 25%, and over 25%.

### Land use

This layer represents the occupation of the terrain, as reported by CORINE Land Cover in 2018, which is related to the limitations imposed by renewable installations on the use of land. It is used as both a limiting factor to the available area for installation and a factor contributing to the determination of suitability. Any land pertaining to CORINE classes 1, 4 or 5 (artificial surfaces, wetlands, and water bodies, respectively) is excluded from installation because of its nature. Different land uses from classes 2 (agricultural areas) and 3 (forest and semi-natural areas) are classified according to their suitability. In this work, we follow the classification proposed in [56] adapted to ratings from 1 to 5 in order to integrate it with the rest of fields.

These independent layers are then linearly combined into a unique suitability index. The main method used is described in Section 3.1.2. Nevertheless, the selection of this method derived from a review of the weights given to these particular factors in the existing literature. The inter-comparison of different studies can be seen in Table B.4, together with the reference study and the final weights applied to the present work.

## Appendix C. Assignation of indices to sustainable development goals indicators

In order to assess the level of agreement of each mix with SDGs, we need to quantify their meeting of the indicators. To do so, we categorize them into discrete indexed divisions. In order to establish these divisions, we take the whole range of optimal scenarios and diagnose their contribution to the SDG indicators. For each contribution, we take its maximum and minimum value for any of the optimal scenarios. Then, this range is divided into five intervals that will transform it
<figure><img src="image_18.png" /><figcaption>**Fig. D.10.** System total cost (in G€, left), mean penetration (in %, middle) and installed capacity (in GW, right, blue for wind and orange for PV) for $\gamma=10$, $\alpha = 3 \cdot 10^{-3} \text{ €MWh}^{-1}$ for the optimal mixes using each of the three suitability definitions: global, social and technological. On the left panel, gray bars represent the system total cost with the corresponding suitability definition and green dashed outlined bars show the system total cost when considering the global suitability cost.</figcaption></figure>

into an index, in increasing or decreasing order depending on whether the aim of the indicator is to increase or decrease a given magnitude, and always considering the lower limit of the intervals inclusive and the upper limit exclusive. In this appendix, we explicitly address the magnitudes used for each indicator, and the divisions considered to transform it into an index from 1 (worst case) to 5 (best case).

### SDG 2.4.1 Proportion of agricultural area under productive and sustainable agriculture

A suitability index for land use of 1 or 2 indicates land that is very suitable for agriculture. We assume that any of this land not destroyed by renewable installations will be used for productive and sustainable crops. We consider the area of fertile land occupied by renewable installations as a magnitude representative of the indicator. The less fertile area that is occupied by renewable installations, the better for the indicator as more area is available for productive and sustainable crops. We consider an index of 5 for an occupation of 840.43 to 1922.13 km²; 4 for 1922.13 to 3003.83 km²; 3 for 3003.83 to 4085.53 km²; 2 for 4085.53 to 5167.23 km²; and 1 for 5167.23 to 6248.93 km².

#### SDG 7.1.2 Proportion of population with primary reliance on clean fuels and technology

Reliance of population on clean energy implies that the renewable energy that enters the system reaches their locations. Using the index for distance to urban nuclei, we add the indices of pixels with installations to identify a measure of installation proximity to end users in a unique magnitude. The higher this value, the closer capacity is to population, and therefore their primary reliance is in these sources. This value can range from 2141750 to 6288360. This is then transformed into an index through even divisions of this interval, with the index increasing with the number.

#### SDG 7.2.1 Renewable energy share in the total final energy consumption

The share of renewable energy in the final energy consumption is the penetration. The higher the penetration, the better the indicator is being satisfied. Since we have an established minimum penetration of around 30%, we define the indices considering this existing threshold. We assign an index of 1 to penetrations of 30%–46%, 2 to 46%–62%, 3 to 62%–78%, 4 to 78%–94%, and 5 to 94%–110%.

#### SDG 7.b.1* Installed renewable energy-generating capacity in developing countries (in watts per capita)

Spain is not a developing country, but still this SDG indicator presents a good reference of the amount of capacity installed to reach renewable generation objectives. The magnitude used to reference this indicator is directly the installed PV and wind capacity per capita,

considering the current population, and considering increasing values positive for the indicator. This value ranges between 793 and 2363 watts per capita, which is divided into five equal intervals, and assigned an index that increases with the magnitude.

### SDG 13.2.2 Total greenhouse gas emissions per year

We estimate the carbon emissions using [86], considering the generation for each renewable technology, and assuming a distribution of dispatchable generation similar to the current one. This yields emissions in tons of CO₂ equivalent. These emissions are then transformed to indices, considering that the goal is to reduce emissions and that the index of the SDG indicator should decrease as emissions increase. These emissions are non-negative and can reach values up to 65 million tons of CO₂ equivalent. Taking this reference, values are then transformed to indices: 5 for 0 to 13 million tons of CO₂ equivalent; 4 for 13 to 26 million tons of CO₂ equivalent; 3 for 26 to 39 million tons of CO₂ equivalent; 2 for 39 to 52 million tons of CO₂ equivalent; and 1 for 52 to 65 million tons of CO₂ equivalent.

#### SDG 15.1.1 Forest area as a proportion of total land area

A suitability index for land use of 3 is indicative of the presence of forest. We assume that any forest land that is not occupied by renewable installations will remain a forest. Therefore, the less renewable installations occupy forest land, the better it is for the SDG indicator. The area of forest occupied by renewable installations ranges from 434.45 to 2320.15 km². An index that decreases as this area increases is assigned to evenly divided intervals marked by this range.

#### SDG 15.3.1 Proportion of land that is degraded over total land area

Assuming that the installation of renewable energy sources is a degradation of land, we take the area occupied by renewable installations over the total land area. As this proportion increases, it is bad for the indicator as more land is degraded. This value ranges between 1.05% and 3.08%. Therefore, we assign an index that decreases with the magnitude in five evenly divided intervals.

## Appendix D. Uncertainty analysis

The identification of optimal VRE deployment scenarios is not devoid of complexities and uncertainties. In this appendix, we delve into the multifaceted landscape of uncertainties that surround optimal deployment scenarios. To design resilient and effective renewable energy strategies, it is imperative to acknowledge and comprehensively understand the various factors contributing to these uncertainties. By doing so, we aim to provide insights that enable more robust decision-making
<figure><img src="image_19.png" /><figcaption>Fig. D.11. Installed capacity distribution in optimal mixes for $\gamma$=10, $\alpha$ = 3 · 10⁻³ ∈ MWh⁻¹ for PV (left) and wind (right) using the full (top), social (middle) and technological (bottom) definitions of suitability.</figcaption></figure>

processes for the development of sustainable energy systems, capable of withstanding the dynamic and unpredictable nature of climate resources in our rapidly changing world.

In an analysis of the uncertainties present in this work we have identified six different sources of uncertainty: the selected climatic source, the model, the ERA5 data, the economic cost of VRE sources, the suitability definition, and the climate timeframe sampling. In this appendix, we discuss each of these sources of uncertainty and their effect on the presented results. Considering that certain sources have already undergone thorough examination within the existing body of literature, this section offers a blend of two approaches: a comprehensive literature review concerning the explored sources of uncertainty, coupled with experimental analysis focusing on elements that pose greater challenges in terms of assessment.

First, in the analysis of the optimal deployment of VRE sources, a critical aspect pertains to the sensitivity of the models to the choice of climate data. As outlined in Tantet et al. [87], the selection of climate data sources may change the outcomes of the optimization, so the comprehensive selection of a quality source of climatic data is crucial. The need for good quality climate data gains importance when considering the sensitivity introduced by some model processes. For instance, corrections of capacity factor series or the calibration of demand require hourly data that truly represents the climatic variables at a given point in time. Otherwise, these processes could just become a source of error amplification.

The consideration of all of the mentioned factors prompted the selection of the ERA5 reanalysis [74] as the climatic data source. ERA5 presents the most accurate climatic information in terms of wind
<figure><img src="image_20.png" /><figcaption>Fig. D.12. Suitability pseudo-cost of installing 100 MW for PV (left) and wind (right) using the full (top), social (middle) and technological (bottom) definitions of suitability.</figcaption></figure>

generation [88], especially in offshore or flat inland locations [89]. From the point of view of PV, ERA5 also gives a good representation of radiation [90] and temperature (especially in mid-latitudes, as in the presented case study) [91]. Despite the good quality of ERA5, it should be noted that its generally good representation of observations can present weaknesses at the scale of wind or PV farm due to spatial representativity of the data. Even if the climatic data is good, the grid points represent wider areas than those occupied by generation farms, and as such may present internal variability. However, this type of uncertainty is intrinsic to the use of gridded data.

An additional layer of uncertainty arises from the estimated costs associated with VRE technologies. A comprehensive analysis encompassing over 300 cost scenarios [92] reveals two primary responses to these costs: firstly, the specific composition of the energy mix exhibits a substantial sensitivity to cost variations, and secondly, the overall system assessments are relatively impervious to alterations in cost assumptions. It is imperative to acknowledge the inevitability of

uncertainty regarding installation costs in the forthcoming years. In our study, we rely on the best-guess estimations [93] and explore various scenarios based on these predictions. Nonetheless, it is important to emphasize that comprehensive depictions of the role of VRE within the system are anticipated to be accurately conveyed, even in the absence of location-specific representations, a factor that lies beyond the scope of this study.

### D.1. Uncertainty introduced by the suitability definition

In our endeavor to assess the model's robustness and reliability within this experimental framework, we conduct an evaluation of its stability against structural changes. This assessment serves as a reference point for quantifying variations in significant model outputs, particularly STC and renewable penetration levels. We introduce two distinct test experiments: the first assigns all suitability costs solely to social factors, while the second shifts the suitability term (as indicated
<figure><img src="image_21.png" /><figcaption>**Fig. D.13.** System total cost (in G€, left), mean penetration (in %, middle) and installed capacity (in GW, right, blue for wind and orange for PV) for the optimal mixes for $\gamma$=10, $\alpha$ = $3 \cdot 10^{-3}$ €MWh$^{-1}$ using each of the three sampling periods: 2016–2020, 2011–2015, and 2006–2010.</figcaption></figure>

in Eq. (6)) to focus on technological costs. The alteration in the suitability definition leads to an increase in mean penetration and overall installed capacity, along with a slight decrease in STC when using the newly introduced suitability definitions (see Fig. D.10). However, when we assess the optimal distributions and their STC under the global suitability cost, we observe overcosts of approximately 5 G€ in the actual STC when considering all factors. These variations push the total STC beyond the maximum STC obtained for this $\alpha$ value using the original suitability definition (slightly under 15 G€). Additionally, it is worth noting that less than half of this STC variation was observed between a scenario allowing unrestricted installation and one that barely permits new installations, representing the two extremes in terms of the $\gamma$ values (refer to Fig. 5 bottom left).

A similar phenomenon is observed when examining mean penetration. Variations in suitability criteria introduce changes in mean penetration, which reaches values up to 70%. This marks the highest mean penetration value achieved by this $\alpha$ value, observed under the $\gamma_0$ scenario. These alterations in penetration would equivalently represent a reduction of over two orders of magnitude in $\gamma$, underscoring the high sensitivity of the system to its fundamental components such as the suitability definition.

To better grasp the source of these disparities, we examine the optimal capacity distributions themselves (Fig. D.11). For PV installations using both social and technological suitability definitions, we observe two significant clusters in the southern and eastern domains, along with a third concentration over the islands. The southern cluster, present in both cases, exhibits minimal overlap, leading to sparse PV installations when considering the full suitability cost. Conversely, the islands show a different pattern, allowing mostly large PV installations under both suitability definitions, matching the full combined suitability cost. Notably, a north-eastern pattern reveals small but widespread PV installations under the social and technological suitability definitions, which do not translate to the optimal scenario under the global approach considering their combination, as evident in Fig. D.12. The unexpected nature of this pattern can be explained by the process involved in the construction of the full suitability, influenced by pixel-level suitability indices and the posterior fitting to a fourth-order polynomial curve.

A similar phenomenon is observed in the case of wind energy, with certain regions exhibiting capacity in two distinct suitability definitions but not in their combinations while the opposite phenomenon takes place in others. In the central northern region, installations that are part of the two optimal configurations based on social and technological suitability definitions do not necessarily translate into the global mix, indicating non-beneficial internal combinations. Conversely, the inverse phenomenon occurs as well: when considering differentiated social and technological suitability, regions in the northwestern, southern, and some isolated eastern areas show wind energy capacity. This

consistent pattern, regardless of the suitability definition used, can be directly attributed to the presence of strong, persistent winds in these regions, influenced significantly by general Atlantic winds in the north and south, and the channeling effect of mountainous terrain in the east. These robust nuclei remain consistent across all suitability definitions, influencing the composition of the global suitability-optimal mixes. However, the emergence of additional isolated nuclei highlights how certain areas may be suboptimal under two distinct suitability definitions but become optimal when considering their combination, owing to the non-linear nature of this suitability definition process.

Significant alterations in the distribution are anticipated when there is a change in the suitability definition, underscoring its pivotal role in the analysis. These findings emphasize the critical importance of accurately estimating all pertinent suitability components to the best of our ability. Failing to do so can result in substantial underestimations of the impact of installations. The original estimate presented in this study provides a straightforward yet comprehensive representation of the most crucial factors influencing installation suitability. Solely considering either social or technological factors would yield an incomplete assessment of land potential, potentially leading to significant errors in determining the optimal installation potential for any given region.

## D.2. Climate timeframe sampling

The sensitivity of the model to climatic sampling indicates that a 5-year period serves as a suitable representation of a given climate [44]. In this study, we have characterized the present climate using data from the 2016–2020 period, as it also begins to reveal patterns for the very near future, aligning with when most of the installed capacity will contribute to the energy mix. However, we also assess the impact of sampling the present climate through two alternative periods (2006–2010 and 2011–2015) to investigate how the chosen period influences the optimization results.

The large-scale descriptors of the system, particularly STC, mean penetration, and total installed capacity, exhibit remarkable similarity among the three sampling periods (see Fig. D.13). This consistency underscores the robustness of our findings and their independence from the particular climate sampling chosen. Nonetheless, recognizing the potential for deriving a global system diagnosis from different distributions, we shift our focus to the optimal installed capacity distributions obtained under the three distinct sampling periods.

An examination of the optimal capacity distribution maps reveals strikingly similar distributions for both PV and wind (see Fig. D.14). Qualitatively, all three sets of maps exhibit virtually identical capacity distribution patterns. On closer scrutiny, minor quantitative differences become apparent, although their impact on the overall system is negligible in all cases. In summary, these findings underscore the high
<figure><img src="image_22.png" /><figcaption>Fig. D.14. Installed capacity distribution in optimal mixes for $γ=10$, $α = 3 \cdot 10^{-3} \in \text{MWh}^{-1}$ for PV (left) and wind (right) using the 2016–2020 (top), 2011–2015 (middle) and 2006–2010 (bottom) sampling periods.</figcaption></figure>

level of robustness to climatic sampling and suggest that this factor introduces only minimal insignificant variations to the overall results.

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