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# Sensitivity analysis of load profiles: implications for resource adequacy in future power system

Valentin Satge, Sophie Gabriel, Cédric Clastres

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Valentin Satge, Sophie Gabriel, Cédric Clastres. Sensitivity analysis of load profiles: implications for resource adequacy in future power system. Energy, 2025, 335, pp.138272. 10.1016/j.energy.2025.138272. cea-05294994

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https://cea.hal.science/cea-05294994v1

Submitted on 2 Oct 2025

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SENSITIVITY ANALYSIS OF LOAD PROFILES: IMPLICATIONS
FOR RESOURCE ADEQUACY IN FUTURE POWER SYSTEM

Valentin Satgé¹²*, Sophie Gabriel¹, Cédric Clastres²

¹CEA/DES/I-Tésé, Université Paris Saclay, Gif sur Yvette, France

²Grenoble Applied Economic Laboratory, INRAE, CNRS, University Grenoble Alpes, France

*Corresponding Author: valentin.satge@cea.fr

ABSTRACT

Ensuring the reliability of future electricity systems requires more than matching annual energy needs—it demands understanding when electricity is used. Traditional resource adequacy (RA) assessments rely on Monte Carlo simulations across many climatic years to capture inter-annual variability, but often assume fixed demand profiles. This overlooks how even small structural shifts—such as increased heat pump use or changing EV charging patterns—can significantly alter system stress and operational outcomes. This study quantifies the sensitivity of RA metrics to such variations. Using ANTARES Simulator and French TSO projections, a European electricity model for 2050 is developed and tested under three scenarios with equal annual demand but different hourly profiles: a reference case, a winter case (2–10% more winter demand), and a peak case (5–20% more peak-hour demand). Results show a 4% winter load increase triples LOLD hours, and 8% causes tenfold more unsupplied energy. Importantly, most stress concentrates in just a few critical climatic years. Identifying these years using simple indicators—like residual load or wind capacity factor—could reduce computational burden without losing key adequacy insights. This study emphasizes that alongside inter-annual variability, accounting for load shape sensitivity is essential for robust and reliable RA assessments in a changing energy system.

# 1 INTRODUCTION

In the context of the energy transition, accurately modeling electricity system is essential to understanding the stakes of this transition and ensuring the reliability of future power grids [1]. Key questions arise around the economic viability, optimal technologies choices, and the primary obstacles to ensuring a secure energy future. As [2] notes, “several studies are limited to supply-side options,” and demand side impacts are often overlooked, thus failing to address the evolving dynamics of electrification.

This growing emphasis on demand-side dynamics raises critical questions, particularly in the face of massive electrification. One major concern is whether the current level of electricity supply security can be maintained as electrification expands. This extensive electrification, driven by new technologies and the shift of sectors like heating and industry to electric power, introduces two main changes: an increase in the annual electricity demand and significant alterations in the demand curve shape [3]. This study focuses on the second less explored aspect: the shape of the load curve. Additionally, emerging demand flexibility and advancements in storage systems are likely to further reshape the system’s characteristics, making modeling even more complex. While many reports coming from governments or global organizations provide valuable insights into projected annual demand, few delve into the granularity of hourly load data or analyze how variations in load shape impact energy system performance. Understanding these effects is crucial for ensuring the reliability and robustness of future electricity system.
## 1.1 Resource Adequacy (RA)

Resource adequacy refers to the ability of the electricity system to supply sufficient power and energy to consumers at all times [4]. In simpler term, achieving RA means limiting the risk of electricity shortfalls within tolerable limits. In the context of France, this “tolerable limits” threshold is defined as an average of 3 hours of load shedding per year [5]. This risk of electricity shortfalls is changing with the increasing penetration of variable renewable energy sources, since the correlation between weather patterns and system reliability becomes even more important and leads to an evolution of RA assessments technics [6].

The main focus of RA assessments was traditionally on peak load hours, based on the assumption that the highest risks occur during these periods [7]. However, the increasing role of intermittent renewables, energy storage, and demand side response has shifted the focus to a broader range of critical hours, leading to the adoption of “representative hours” to better assess system adequacy. This approach aims to capture key operational patterns but has limitations, as it may fail to account for rare but high-risk events that occur only in specific years. To address this, [8] introduced “resiliency hours”, expanding the number of hours analyzed to improve coverage of extreme conditions while keeping computational costs manageable. Still, when feasible, using an entire year of hourly data remains the most robust approach to have efficient RA assessments [4], as it allows to add inter annual variation of the system. The evolution of RA approaches also shapes the way RA is modeled. RA is typically assessed using probabilistic methods, such as Monte-Carlo simulations, which model system operations across multiple years to capture the inter-annual variability of both demand and supply at an hourly time step [4]. A comprehensive RA assessment requires both a large number of climatic years to account for inter-annual variations and an extensive set of representative hours – ideally all hours or at least “resiliency hours” – while also accounting for planned and unplanned outages.

By integrating probabilistic approaches with the advancements mentioned above – such as representative periods or resiliency hours – these methods enable a more robust evaluation of system adequacy. The combination of time resolution improvements and probabilistic modeling forms the foundation of modern RA assessments, as emphasized in key studies by [4,8,9]. These studies also inform the methodology of this work and guide its exploration of load shape sensitivity in RA assessments.

Thus, one of the strengths of RA analysis lies in their ability to capture inter-annual variations, including colder or windier years, and the shifting correlations between renewable generation and demand. However, while inter-annual variability accounts for natural fluctuations in climate and weather, it does not address deeper structural changes in the energy system that may significantly alter the load shape over time.

## 1.2 Limitation of RA for future systems with structural changes

Traditional RA assessments rely on historical years to model different climatic conditions, assuming that future variations will closely follow established patterns with minimal structural shifts. However, this assumption becomes problematic when key technological or societal changes reshape electricity demand in ways that historical data cannot fully capture. Two primary factors can structurally alter the load profile for forecasting studies, directly affecting system adequacy. The evolution of assumptions coming from reality shifts for some penetration of technologies linked to societal or political behaviors is one. Also, methodologies used for long-term load forecasting is another.

1. **Assumptions shaping the load profile:** Different structural assumptions about the deployment of key technologies, such as electrification of heating or transportation, influence the overall shape of the load curve [10]. As mentioned by [11], social, environmental or political constraints introduce uncertainties that challenge the original assumptions. These elements bring uncertainties around the main assumptions and could lead to a divergence for the profile of the load if the initial assumptions are not respected. Additionally, many studies rely on historical load patterns as a proxy for future demand shapes [3,12–16], further increasing the risk of misalignment with emerging consumption behaviors driven by new technologies and evolving societal norms.
2. **Forecasting methodology:** The methodologies and inputs used in forecasting might significantly affect projected load shapes, particularly under future scenarios where demand profiles may diverge from historical patterns. The choice of forecasting tools and the treatment of uncertainty could greatly affect the reliability of RA assessments, as bottom-up, top-down or machine learning technics are different technics of load forecasting [12,17–20]. As stated by [21], the load is influenced by three characteristics: calendar, weather and socio-economics, with a lesser focus on the last aspects that can bring differences methodologies. Moreover, as [21] points out, the “literature remains scarce for hourly mid-term forecasts”, highlighting a critical gap. This scarcity contributes to uncertainties in system modeling and underscores the need for continued development of robust mid-term forecasting approaches to better support long-term planning and resource adequacy assessments.

Structural changes to the load shape, whether due to methodological or system changes, could have a significant impact on system adequacy.

This illustrates that while varying climatic years provides useful insights, it cannot address deeper shifts in load shape driven by structural changes and then bring questions about RA assessments of models during forecasting studies.

Thus, the objective of this paper is to address an important gap in the literature. While different studies explore the impact of climatic variability by modeling multiple weather years [4,8,9], few, if any, assess how structural shifts in load profiles – even small ones – can compromise the adequacy of an electricity system that was originally deemed resource-adequate. To the best of the authors’ knowledge, no previous work systematically analyzes the sensitivity of RA metrics to small, plausible deviations in the demand profile using multi-year climatic modeling.

The purpose of this study is not to generate detailed new forecasting scenarios; rather, it is to
demonstrate that even within an established future scenario, minor changes to load assumptions – such
as variations in the degree of electrification or behavioral adoption of flexibility – can substantially
degrade system adequacy and then raise questions on the future capacity mix.

By focusing on sensitivity analysis after scenario definition, this work highlights those structural uncertainties in load shape may pose risks that are not captured simply by considering inter-annual climatic variability. In doing so, the study emphasizes the need to integrate load shape sensitivity testing more systematically into future RA assessments, particularly in long-term energy planning exercises where forecasting uncertainties are high.

The remainder of the paper is structured as follow. The Section 2 explains the followed methodology, by briefly explaining the tool ANTARES Simulator, then the choice of the inputs and assumptions, to finally explain the scenario taken in this study. The Section 3 focuses on the results arising from the model and a discussion is made. Finally, Section 4 concludes the study and discuss about the limitations and future work.

## 2 METHODOLOGY

In this study, we investigate the impact of small variations in the electricity load profile, due to structural
changes, on a resource adequate system. To do so, a European electricity model is developed based on
the French Transmission System Operator projection for 2050 [22]. This model is designed to meet the
probabilistic criterion of a maximum of 3 hours annual of load shedding and is constructed to be
sufficiently representative for conducting sensitivity analysis. Similarly to the approach taken by [9],
this study does not aim to develop new optimization technics or method of modelling. Instead, it
leverages existing models and datasets to focus on understanding the role of one critical variable in
energy modeling: electricity profile demand. A particular focus is made on the French power system.
In this section, we first present the model used for the optimization in Section 2.1., then a focus is made
on the creation of the system studied in the Section 2.2., followed by the selection of scenarios in the
Section 2.3.
## 2.1 ANTARES Simulator

ANTARES simulator is the economic dispatch model used in this study [23]. Developed by RTE, the French TSO, ANTARES Simulator is designed to simulate the demand-supply equilibrium of a power system. It operates as a unit-commitment model, optimizing the system at an hourly time step over one calendar year. It allows for multi-years simulations using a Monte-Carlo approach to capture various conditions and uncertainties, such as different climatic years, or different kind of outages – planned or unplanned [24]. Additional information is available in the Supplementary Material A.

## 2.2 System studied / Input data and assumptions

Since the tool ANTARES Simulator does not provide a predefined dataset for the European system, a new model, ESMOD2050 was developed to represent a plausible European electricity system by 2050. The dataset must include a range of essential information: hourly time series data for load and renewables generation across many European countries and numerous climatic years, in order to provide insightful RA assessments.

Because full datasets describing a European electricity system in 2050 are scarce thus study combines three main sources:

* The French TSO's forecasting report [22] that provide detailed annual values for France and neighboring countries (Germany, United Kingdom, Spain, Italy...), along with aggregated data for a wider European region [25]. However, this source only offers annual data, which is insufficient for the modeling needs, and do not consider all of the European countries.

* The ENTSO-e ERAA dataset [26] supplies 35 historical climatic years of load and renewable production data (1981-2016), normalized to match projections for 2024, 2025, 2027 and 2030. In this study, bidding zones are aggregated to one node per country to simplify the modeling.

* The OSMOSE dataset [27] complements these sources by providing long-term projections for installed generation capacities and cross-border interconnections across Europe.

Although relying on multiple sources is not ideal for data consistency, this is necessary to create the model for 2050. More information is available on the inputs and assumptions in the Supplementary Material B.

This study employs a unique system power mix, which might raise questions regarding system sensitivity, as this can vary based on system characteristics. While testing less flexible power mixes could reveal higher sensitivity to load variations, the current setup already represents a relatively robust case and might already overestimate the robustness of the system. Indeed, the LOLD for France is inferior than three hours in average for the different climatic year, and the chosen power mix remains relatively flexible compared to other European projections. France maintains over 35 GW of nuclear capacity, and gas power plants are available in multiple countries with an important assumption about the total availability of enough 'green gas' at any moments. Demand-side flexibility is set at 8% of the daily consumption for each day, with the possibility of the consumption to be used anytime in the day - a plausible yet significant factor in system stability. Additionally, interconnections modeled from the Osmose project and RTE scenarios enhance overall flexibility. Moreover, the study focuses on load shape changes for France, whereas large-scale European electrification – such as widespread heat pump adoption – could amplify thermos sensitivity across the entire system. In such cases, reduced export availability during peak hours could further increase system stress, highlighting the need for future studies focusing on load variation on numerous European countries and not only one of them. Thus, the conclusions made on this study can be transposed to other power mix since a small variation here might lead to higher variations in a less flexible system.

## 2.3 Scenario design

As noted in the introduction, the shape of the load curve is heavily impacted by the extensive electrification associated with the energy transition. This shift may result from increased electricity demand in heating, industrial electrification, or the transition from combustion to electric vehicles. This
study focuses on two key factors anticipated to have the greatest impact on the load curve: residential electrification and the rise of electric transportation [2,28].

For the residential part, two primary studies [29,30] highlight the main factors influencing residential consumption and load shape. Rather than investigating each household appliance individually, these studies focus on two variables: the type of heating (heat pumps or electric boilers) and the insulation quality of buildings [29].

Heating demands have a significant impact on the residential load, especially during winter. Building with poor insulation require more electricity to maintain comfortable indoor temperatures, increasing both total winter consumption and the seasonality of the demand [30]. Additionally, inefficient heating systems, such as less effective heat pumps or electric boilers, raise electricity consumption during heating hours, thus increasing the winter demand and the peak load hours. Two different scenarios characterized by different adoption rate of heat pumps and high retrofit rate for the insulation of houses are implemented by [30]. In the “optimistic scenario” of this study, for both the deployment of heat pumps and insulations of houses, the peak demand increases up to 37% and the annual demand increases by 19% compared to the historical data from 2016 – year chosen for the availability of its data in the study by [30]. For the less optimistic scenario, these increases could rise to 53% for peak demand and 27% for annual demand. This 16% difference in peak load and 8% in annual demand from the two scenarios underscores how sensitive the load shape is to key assumptions about technology penetration and efficiency. Changing habits or the adoption of new technologies can significantly reshape both peak and winter electricity consumption.

Consequently, this study considers the insulation of building and the adoption of electric heating technologies as key variables influencing residential demand patterns, and thus, total load shape.

For transportation, the integration of electric vehicles will significantly reshape future electricity profiles [31]. Thus, understanding charging habits are essential for long-term assessments. However, EV charging profiles are frequently treated as static inputs [32]. The selected profiles remain unchanged throughout the study period, despite being influenced by various factors such as EV penetration, charging infrastructure, vehicle efficiency, thermal sensitivity or user habits... Also, the thermal sensitivity of electric charging, with the decrease of battery efficiency in winter days, might be important in the load shape of charging EVs [33]. Any change in these variables could alter the load profile and the multitude of influencing factors increases the likelihood of deviations from the initial assumptions.

Therefore, this study considers the charging habits and penetration of electric vehicles as key variables influencing the load shape of transportation, and thus, the total load shape.

The residential demand evolution and the transportation are the two key factors influencing the load profile in the scenario created. Adjustments to these two sectors are used to explore variations of the load shape from initial assumptions. For the residential sector, these changes could come from a different speed in the building renovations or differences in heating technology adoption [30]. For the transportation, the penetration of EVs and charging habits are the two primary sources of change [32]. As a result, three main scenarios are defined: the *reference case*, the *winter case*, and the *peak case*, with sub-scenario for each of them to capture variability.

In each scenario, only the shape of the load curve is modified, with the primary assumption that the annual electricity demand remains constant across all cases in order to isolate the effects of load curve variations. This approach aligns with some model cases by [3], where demand variability is decreased or increase, relative to its reference case, using historically shaped data, with the goal of getting the impact of a different variability on the system.

* *Reference scenario:* see Section 2.2

* *Winter scenario:* This scenario models an increased winter seasonality of the consumption potentially reflecting at the same time slower building renovation rate, accelerated heating electrification or a higher EV adoption that amplifies winter thermal sensitivity. Five-sub scenarios are created, each increasing winter load by increments of 2%, ranging from 2% to 10%. This maximum 10% increase is based on findings by [30], which estimate that winter-
only consumption could rise by 19% and 27%, depending on assumptions about heating electrification – see ‘residential part’ for more information. This 8% variation serves as a basis for defining temperature-sensitivity sub-scenarios. To maintain constant annual demand, consumption is increased during the “cold” months (October to March) and proportionally reduced in the remaining months.

* **Peak scenario:** This scenario models the increase of electricity consumption during peak load hours. It could reflect a potential increase in the penetration of heat pumps, less efficient way of electrifying the system or shift in charging EVs habits, such as higher proportion of immediate charging upon arrival at home [34]. Four sub-scenarios are included, with peak-load increased in 5% increments, ranging from 5% to 20%. Similarly to the winter-scenario, these increments are based on findings by [30], which suggests that peak load hours could range from 37% to 53% increased relative to historical data. This 16% variation has been extended to 20% to account for possible divergence from sector beyond heating electrification. Consumption is increased from 4PM to 10PM in “cold” months (October to March) and proportionally decreased in the remaining months for all hours.

Similarly to the winter case, a summer case was tested by increasing the load during the summer months (June-September) by up to 10%. However, the results show no significant impact on system adequacy: the adequacy metrics – LOLD, unsupplied energy, remain unchanged. This outcome is consistent with the focus on France, where adequacy challenges are primarily concentrated in winter due to the thermosensitivity of the load. These findings suggest that, for this case study, summer load variations are of secondary importance.

As a result, the summer scenario will not be further analyzed in detail in this paper. Nevertheless, this type of analysis could be highly relevant for regions such as Spain, Italy, or California, where summer represents the most critical period for system stress.

<table><caption>**Table 1:** Summary of the different scenarios in the study</caption><tr><td><strong>Reference Scenario</strong></td><td>-</td></tr><tr><td><strong>Winter Scenario</strong><br>Winter months (Nov-Mar) consumption raised<br>Non-winter months consumption adjusted downward to keep total energy constant.</td><td>Winter [2%-4%-6%-8%-10%]</td></tr><tr><td><strong>Peak Scenario</strong><br>Load raised during winter peak hours (4-10 pm);<br>slight decrease in load elsewhere to balance annual consumption</td><td>Peak [5%-10%-15%-20%]</td></tr></table>

# 3 RESULTS AND DISCUSSION

This section is divided into three sub-sections. The first examines the system's sensitivity to different load profile scenarios, highlighting the impact of small variations on resource adequacy metrics. The second sub-section focuses on the importance of incorporating multiple climatic years in resource adequacy assessments. While challenging years play a disproportionately large role in system performance, identifying and focusing on these specific years could help reduce computational demands without compromising analysis accuracy. Finally, simple metrics are implemented in order to decrease the computational burden of taking numerous climatic years, yet still keeping the most important years.

## 3.1 Evolution of the results depending on the scenarios

This study analyzes the impact of load profile variations on resource adequacy metrics across multiple scenarios, while comparing the result to a resource-adequate reference system. Figure 1 illustrates the evolution of the LOLD and the unsupplied energy across scenarios, providing several layers of
information. The dots correspond to the LOLD for each climatic year. The shape of the violins depicts the distribution of these dots across all climatic years while the red dotted lines represent the average LOLD value for each scenario. Flatter violins indicate fewer “difficult years” within a given scenario, whereas higher violin highlights the presence of scenarios with difficult years – the LOLD can reach more than 30 hours for a unique climatic year in several cases. In the reference scenario, the LOLD is 1.4 hours, the lowest among all cases. Sensitivity analysis reveals that LOLD increases across all sub-scenarios, ranging from 2 hours in “Peak 5” to 12.7 hours in “Winter 10”. Notably, a 4% increase in winter consumption (“Winter 4”) triples the system’s LOLD, while the unsupplied energy in the “Winter 8” scenario is amplified tenfold compared to the reference case. These findings underscore the system’s vulnerability to even small variations in load profiles and emphasize the critical need for sensitivity analyses in resource adequacy assessments.

<figure><img src="image_3.png" /><figcaption>**Figure 1:** LOLD and unsupplied energy for the two main scenarios (winter in blue and peak in orange) and all of its sub-scenarios.</figcaption></figure>

An interesting observation emerges when comparing the sensitivity of the system in “peak” versus “winter” scenarios. Traditionally, peak periods have been considered the most critical for system adequacy, which is why models such as TIMES typically divide time slices into peak, baseload, and off-peak hours across different seasons [35], without taking into account the 8760 hours of the year. However, such approaches often overlook the dynamic nature of demand and its interaction with variable generation. In contrast, this study reveals that a 15% increase during peak hours leads to lower system stress than a 6% increase across all winter hours – almost 7 hours of average LOLD and 75 GWh of unsupplied energy for “Winter 6”, against 5.9 hours and 51 GWh of LOLD and unsupplied energy for “Peak 15”. Two factors may explain this phenomenon. First, the total energy increase in “Winter 6” exceeds that of “Peak 15” (21 TWh vs. 14 TWh). Nevertheless, the temporal distribution of increased demand might play a crucial role as an increase in peak hours would not have the same impact in the adequacy of the system as an increase during night hours. However, while peak load hours are conventionally considered the most vulnerable, Figure 2 highlights that system stress is not confined to these hours. Early morning (5-9 AM) emerge as critical periods in the reference case, and the increase in all hours amplifies this criticality for “winter” scenarios. For the Peak Scenario, a slight decrease appears compare to the Reference Scenario during these hours. This reduction is explained by the scenario design, where non-peak hours – including early mornings – experience a slight load decrease to preserve identical annual consumption across scenarios. Similarly, high winter scenarios also reveal sensitivity during night hours, a time typically associated with lower system stress. The only moment in the day when there are minimal adequacy issues appear during middays, when the photovoltaic production is at its highest.
These results highlight the shifting nature of adequacy challenges in future energy systems dominated by renewables and underscore the importance of detail temporal analyses in RA studies since the peak load hours are not the only difficult moments for the grid. Thus, a focus is made on the winter modification, more than for the “Peak Scenario”.

<figure><img src="image_4.png" /><figcaption>**Figure 2:** Evolution of the unsupplied energy depending on the hour of the day and for each sub scenarios</figcaption></figure>

To investigate why certain climatic years remain problem-free under the “Reference Shape” scenario, but face issues under another, it is insightful to examine a typical period of grid stress. Analyzing challenging moments in this modeling reveals that system difficulties frequently arise during conditions of low wind production, high electricity consumption and limited import capacity [36]. This observation is quantitatively validated by Figure 3, which demonstrates a strong correlation between low wind capacity factors and occurrences of unsupplied energy. As wind capacity factors decline, the likelihood of unsupplied energy events increases significantly. Across all scenarios, only a single unsupplied energy event occurs when the wind capacity factor exceeds 40% - and this happens exclusively in the “Peak 20” scenario. These findings reinforce the conclusions drawn from Figures 1 and 2, which indicate that unsupplied energy is not confined to traditional peak hours. Instead, the correlation between low wind availability and system inadequacy suggests that increases in load at any hour – even during off-peak times – can trigger supply shortfalls. This explains why non-traditional periods such as night hours emerge as critical, as evidenced in Figure 2, where unsupplied energy is observed during night hours. Raising demand at any hour increases the risk of overlap between low wind generation and peak system stress. Such outcomes, while uncommon under today’s system configurations, could become more frequent in future systems dominated by variable renewable energy sources and higher thermo sensitivity. Overall, the results confirm a strong correlation between low wind production and periods of imbalance in the system.
<figure><img src="image_5.png" /><figcaption>**Figure 3:** Correlation between the unsupplied energy and the wind capacity factor for each sub scenarios.</figcaption></figure>

To illustrate these dynamics, a week representing the year 2050 of this system in January (January 18-28) from the climatic year 1993 is analyzed. This period is characterized by a significant drop in wind production from January 22 to 26, as depicted in Figure 4. This figure provides an hourly breakdown of load (dark blue line) and production (colored areas) for the three scenarios: “Reference Shape”, “Winter 10” and “Peak 20”. During this period, the deficit in wind generation (light blue) is offset by increased electricity imports (grey), which stabilize the grid in the “Reference Shape” scenario. However, in the “Winter 10” and “Peak 20” scenarios, unsupplied energy (red as negative values) appears, highlighting the system’s vulnerability under these conditions. When zooming in this graph, it can be seen that the storage (from hydraulic and battery) is at its maximum for the most tensed hours. It is interesting to see that for the “Peak 20” scenario, the unsupplied energy does not spread out of the peak hours, whereas in the “Winter 10” scenario, the unsupplied solution last for multiple following hours.

<figure><img src="image_6.png" /><figcaption>**Figure 4:** Consumption and production for three scenarios (Reference case, “Winter 10” and “Peak 20”). In red, the unsupplied energy.</figcaption></figure>

It is worth noting that the results reveal the system's main margin lies in export/import capacities. Dispatchable thermal clusters are fully utilized and cannot provide additional support. Similarly, demand-side response (DSR), which models industrial load reduction, is already nearing its maximum capacity during the critical periods. Flexibility in demand also shows limited contribution, as the load is already shifted during the middays in order to maximize the use of solar production. This tension in the grid was not seen for the “Reference Shape” scenario; yet, a small variation of the load was able to lead to unsupplied energy, since no margin was available at that moment.
This analysis reveals that one of the system’s vulnerability lies in navigating prolonged periods of low wind production, especially during high demand condition, also called “Dunkelflaut” [36], and confirming the conclusion made in Figure 3. While the reference scenario might handle these conditions adequately, the increased stress from additional winter or peak load demands in other scenarios can push the system beyond its limits, which is what happens in January 23rd and 24th in this example.

## 3.2 The importance of taking multiple climatic years

After demonstrating the system’s sensitivity to small load variations, an additional analysis examines the importance of incorporating multiple climatic years. As emphasized in the introduction and methodology, using multiple climatic years is crucial for robust RA assessments. This analysis aims to understand how different climatic years affect system reliability.

The evolution of difficult climatic years – years in which LOLD occurs – provides key insights. In the reference scenario, only four climatic years contribute to all observed LOLD events, underscoring the importance of modeling a large dataset. Figure 5 illustrates the emergence of new difficult years in each sub-scenario, marked by annotations such as “+14 climatic years”. In the “Winter 6” scenario, six new difficult years appear when the load is increased, while it goes up to nine new difficult years for the “Peak 10” scenario. These results highlight that a smaller dataset might have over estimate or under estimate the adequacy of the system, by capturing few difficult years or by excluding them, leading to an incomplete representation of system vulnerabilities.

Another interesting result lies in the distribution of LOLD hours. While the reference case maintains an average LOLD of 1.4 hours – below the three hours threshold – it reaches between 7 and 18 hours in the four difficult climatic years from the reference case. This supports concerns about the limitations of LOLD as a metric, as previously discussed in [37]: the LOLD is not distributed in numerous but concentrated in a few climatic conditions.

Overall, the concentration of LOLD in just a few climatic years, combined with the emergence of new difficult years in sensitivity scenarios, reinforces the necessity of modeling multiple climatic years to accurately capture system stress conditions.

However, Figure 5 reveals another key finding. In this figure, each sub-scenarios are represented by two histograms: one showing unsupplied energy for the four initially critical years (blue) and the other for new difficult years emerging due to load shape variations (orange). Despite the appearance of up to 14-22 new difficult years in the most extreme scenarios, the majority of additional unsupplied energy remains concentrated within the original four difficult years from the “Reference Scenario”.

For instance, in the “Winter 6” scenario, the six newly difficult years account for only 14% of the additional unsupplied energy, while the original four years still dominate with 86% of the new unsupplied energy. Similarly, in the “Peak 10” scenario, the nine new difficult years contribute just to 5% of the total unsupplied energy for this scenario, with nearly 95% of the increase occurring in the same four years. These results lead to two main conclusions. First, while load variations can introduce a significant number of newly difficult years, their overall contribution to unsupplied energy remains relatively minor compared to the system’s existing vulnerabilities. Second, system stress appears to intensify primarily during periods that were already problematic in the reference case. In other words, increasing demand across various hours does not fundamentally create new risk periods but rather exacerbates stress during times that were already critical, highlighting the concentrated nature of system fragility.
<figure><img src="image_7.png" /><figcaption>**Figure 5:** Unsupplied energy contribution of the four initial difficult years (orange) and the new difficult years (blue) for each sub scenario</figcaption></figure>

These results underscore the dual importance of modeling multiple climatic years to identify rare, high-stress periods while also recognizing that a small subset of years often dominates the system's vulnerabilities. Modeling numerous climatic years is essential during the initialization phase to capture the most critical moments for the system. However, once these “difficult years” are identified, focusing exclusively on this subset can be sufficient to improve system adequacy. This approach not only reduces the sample size for analysis but also significantly decreases the computational burden for sensitivity studies.

## 3.3 Was it predictable without having to run the entire dataset?

Decreasing computational complexity in system energy modeling is a key topic in the literature. The trade-off between the number of technologies modeled, the temporal resolution of simulations, and the number of simulations – specifically, the number of climatic years used is highlighted in [40]. Increasing the number of weather years typically necessitates reductions in time-step resolution or technological detail, and vice versa.

While a major conclusion of this study is twofold – first, that multiple climatic years are essential to capture the full range of system stress conditions, and second, that only a small number of years tend to dominate unsupplied energy events – the identification of these “difficult years” still requires running the full simulation across all weather years. Using a full dataset of different climatic years limits the practical applicability of doing sensitivity analysis of the shape of the load.

This section explores whether it is possible to anticipate the most critical years using simple, easily computable metrics, without running full-scale simulations. The focus is on identifying the four critical years found in the reference “Normal Shape” scenario and the two additional difficult years that appear in the “Winter 4” scenario. The question is whether these years can be flagged using input-based indicators – such as low wind capacity factors or high residual loads – without relying on full simulation results. This reflects a broader research motivation, as seen in studies like [26], where only one climatic year (with the lowest wind capacity factor) was selected to reduce complexity. This section tests relevance of that approach and whether similar proxies can be applied more systematically.

As shown in the Figure 3 and 7, low wind production strongly correlates with adequacy issues. Consequently, the two proposed indicators are closely tied to wind conditions, with a focus on France's wind capacity factor. To assess the effectiveness of these proxies, two temporal resolutions are considered:
* Annual metrics, based on average values over the full year.

* Winter-focused metrics, concentrating on the winter months, which exhibit the highest levels of system stress in this study.

A reminder is made in the Supplementary Materials C for the formula of the residual load and intermittent production.

The methodology is straightforward: for each metric and temporal resolutions, climatic years are ranked from least to most favorable. If the different difficult years consistently appear at the top – in the first half –, the metric may serve as a useful proxy for reducing computational complexity.

Figure 6 illustrates these results for the annual and winter time steps, analyzing both wind capacity factors and residual load. Red markers indicate the four initially difficult years, while orange markers highlight the additional difficult years emerging in the “Winter 4” scenario.

Overall, the findings are interesting. The most problematic years consistently rank within the worst performing half of each category – below the red dotted line, representing the median rank threshold, often appearing in the worst ten across all subcategories, though with some variation. A particularly notable case is Year 30: while it ranks only 22^nd^ and 12^th^ in annual and winter wind capacity factors, it jumps to 3^rd^ and 2^nd^ place when considering residual load – a much stronger predictor of system stress. Additionally, shifting from broader indicators – annual wind capacity factors – to more targeted metrics – such as residual load during winter months – results in a tighter clustering around the most critical years, thereby improving the identification of system stress period. This suggests that residual load is a more effective indicator than wind capacity factor alone and focusing on winter months further improves accuracy. While this approach could potentially halve the number of climatic years required for resource adequacy studies in this case, further refinement may still be needed to balance computational feasibility. Nevertheless, as an initial proxy, this approach could serve as a practical compromise when balancing the need to include multiple climatic years for robust adequacy assessments against the associated computational burden.

<figure><img src="image_8.png" /><figcaption>**Figure 6:** Ranking of the different difficult years depending on capacity factor and residual load for annual and winter time scale. Red dots represent the four initial difficult years (from the Reference Scenario), and in orange, the new difficult years appearing in “Winter 4”.</figcaption></figure>
# 4 Conclusion and future considerations

This study investigates the sensitivity of a resource-adequate power system to small variations in the load profile. Using a unit commitment model, ANTARES Simulator, the European electricity system is simulating across 33 climatic years, analyzing two main scenarios with nine sub-scenarios of load variation. The findings highlight several key insights.

The system exhibits a high sensitivity to load variations in load profiles. In particular, the evolution can be seen in the LOLD metric, where a 4% increase in winter demand ("Winter 4") triples the LOLD, but also in the total unsupplied energy where an 8% increase ("Winter 8") results in a tenfold increase in unsupplied energy. The results also show that increased thermos sensitivity of the system poses a greater risk than variations in peak load hours. The correlation between low wind capacity factors and high electricity consumption creates additional stress periods, notably during early morning (5-9 AM) and nighttime hours, while midday hours remain the most resilient due to significant solar production. These findings indicate that one of the system's key vulnerabilities lies in navigating prolonged periods of low wind generation during high-demand conditions.

The importance of incorporating multiple climatic years in RA assessments is another critical takeaway. A diverse range of climatic years ensures the model accounts for different meteorological conditions, helping to build a robust adequacy assessment. The results suggest that relying on a small number of climatic years could lead to an oversight of critical stress events, which only appear in a subset of years. The majority of new unsupplied energy originates from the same initial most critical years. While including multiple climatic years enhances accuracy, it also significantly increases computational complexity. In order to decrease this computational complexity while keeping an interesting number of climatic years, two complementary results might allow to decrease the total of climatic years needed. First, even as additional challenging years emerge in various scenarios, unsupplied energy remains largely concentrated in the most critical years from the reference case. This suggests that rather than uniformly expanding the number of climatic years, prioritizing the identification and refinement of these key years could offer a more efficient approach. Future research could explore whether improving the accuracy of these specific years leads to an overall reduction in LOLD across the entire dataset. Second, using the first results show that it might be interesting to use metrics that allow to find the difficult years with input metrics. Simple metrics such as wind capacity factor or residual load for annual or seasonal time steps allow to correctly find these difficult years by dividing by two the total of climatic years needed in order to get the most interesting years.

Since the conclusion of this paper is twofold: having a high number of climatic years is important but the difficulties lie in the same climatic years, using simple metrics like wind capacity factors or residual load for seasonal or annual values allow to decrease the number of climatic years.

Some limitations arise in this study and could be tackled in future work. Future work could focus on developing a systematic approach for generating detailed load profiles, rather than modifying them manually. A more precise modeling tool would enable a quantitative assessment of specific variations, such as the impact of a certain percentage of increase in heat pump adoption or a slower than expected building renovation rate. This would provide a more refined analysis of how structural changes in electricity demand influence system adequacy.

The sensitivity of the system might be underestimate since only the shape of the French load is modified. However, policy shifts across multiple countries could lead to similar load variations elsewhere, potentially synchronizing stressful periods and further amplifying the impact on system adequacy.

This approach is reproducible for other countries, allowing for the creation of similar scenarios to assess different types of demand variations. For instance, cooling demand may be a greater concern in regions like Italy, Spain or California.

The European power mix used in this study is constructed from multiple sources. While this approach ensures consistency with existing projections, different power mixes may exhibit varying sensitivities to climatic conditions and load variations. Some configuration could be more resilient to extreme events, while others might be more vulnerable. Future research should explore whether the observed trends hold across alternative power mix scenarios.
Finally, using a capacity expansion model to define an economically optimal system might be a next step for future research. Focus could be made on the different mix obtained depending on the shape of the load, or the difference of system costs when slight variations appear in the load profile.

**CRediT authorship contribution statement**

**Satgé Valentin:** Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data Curation, Writing – Original Draft, Visualization. **Gabriel Sophie:** Conceptualization, Methodology, Resources, Writing – review & editing, Visualization, Supervision, Project administration. **Clastres Cédric:** Conceptualization, Methodology, Resources, Writing – review & editing.

**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.

**Acknowledgments**

This work received financial support by Commisariat à l'Energie Atomatique et Aux Energies Alternatives, a French government-funded public research organization. The authors claim no conflict of interest. We'd like to thank Valentin Richard, Emma Moulan, Sergio-Léo Vargas Aranda and Erica Ramirez for their help with the visualization part of the results, their insights of the model or their helpful discussion.

**Declaration of generative AI and AI assisted technologies in the writing process**

During the preparation of this work, the author(s) used "MistralAI" in order to refine the English language and the clarity in this manuscript. After using this tool, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the published article.

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