Photovoltaic Consumption Modelling of a Construction Materials Factory for Sustainability-Based Sizing Strategy

Abstract

Challenges caused by climate change increase concern for achieving global sustainability. Although citizen awareness is increasing, ensuring sustainability in key sectors like construction is necessary. Achieving sustainability requires essential actions that, however, could have a negative impact on economic performance. Studies on renewable energy installations tend to prioritize performance or sustainability, rather than facing the strategic challenge to find the balance between both. The present work fits this framework through managing renewable energy operations in a construction materials factory of Grupo Puma, located in Spain. The objective of the proposed methodology is to identify key performance indicators (KPIs) for the FV installation and to simulate energy flows using a validated model within a digital simulation environment. This study proposes a trinomial of KPIs—self-consumption, solar utilization, and avoided CO₂ emissions—as more stable indicators than conventional metrics. The Pareto front analysis shows that self-consumption can be increased by up to 20% with only an approximate 10% reduction in solar utilization. This finding offers a clear strategic recommendation: prioritizing higher self-consumption is a viable industrial strategy to enhance Grupo PUMA’s sustainability performance while maintaining acceptable economic efficiency.

1. Introduction

Overpopulation and the accelerating pace of urban life are driving the concentration of human activities in cities and densely populated areas, resulting in significant environmental impacts [1,2], with the construction sector, which plays a pivotal role in driving economic and social development [3], playing a central role due to its substantial demand for materials and energy [4].

Firstly, regarding material consumption, concrete is the most widely used building material globally. All over Europe, more than 5500 companies with around 8000 production plants are producing concrete products which consume large quantities of aggregates and generate voluminous amounts of concrete wastes, generally about 1–2% of the total production volume [5]. Nowadays, the scientific community is developing research that optimizes the selection of materials in order to implement recycling actions of materials in the field of the circular economy [6]. All this minimizes the impact of the consumption of materials in the sector, aligning with decarbonization and circular economy criteria. In the European Union, the construction sector is responsible for a third of European waste production, and specifically the production of construction and demolition waste (CDW) annually amounts to 850 million tons [7]. Regarding the circular economy of construction materials, recycled aggregates from CDW aggregates have been widely studied [8]. Previous authors have confirmed that this material can be applied to engineering infrastructures or buildings, ensuring not only technical but also environmental viability confirmed by applying Life Cycle Assessment (LCA) methodology that allows us in a holistic way to evaluate the environmental impact of the simulated system through the inventory and based on certain impact categories [9]. The use of this methodology is recognized by other authors who confirm that it is essential when it comes to minimizing the impact of construction sector, evaluating aspects such as the embodied energy of buildings, the energy consumed during material production and the evaluation of the entire life cycle of materials used by applying LCA [10].

Secondly, regarding energy consumption, as highlighted by [10], the building sector alone is responsible for approximately 40% of global primary energy use. Furthermore, ref. [11] note that the broader engineering and construction sectors account for 36% of final energy consumption and 39% of CO₂ emissions. In this context, integrating renewable energy technologies such as photovoltaic systems into manufacturing operations offers a significant opportunity to improve energy performance and reduce emissions and environmental impact [12]. Industrial facilities are especially suitable for PV installations due to large roof areas and daytime load profiles, which enable high self-consumption. Recent studies show that on-site PV can cover 20–50% of industrial electricity demand while significantly lowering CO₂ emissions [13].

Other researchers have evaluated the impact of different measures on energy efficiency of buildings [14] and studied the relationship between embodied energy and operational energy. In the mentioned study, different options using multi-objective optimization were applied, deducing the optimal solution for maximum energy efficiency in Swedish residential buildings, concluding the effectiveness of using multi-objective optimization to minimize energy use.

In that sense, the concern for decarbonisation of the energy sector is setting a trend. It is essential to achieve a future net-zero energy system, and it is a key aspect to adopt sustainable energy technologies. In this context, for citizens to contribute to achieving clean energy and for institutions to succeed in developing nearly zero-energy districts and communities, a complex combination of facility design and modernisation, renewable energy sources and energy storage systems is needed [15]. Recognizing the gravity of the climate crisis, the international community has demonstrated a unified commitment to addressing this challenge through the adoption of the Paris Agreement. This landmark accord encourages global collaboration and action towards substantial reductions in greenhouse gas (GHG) emissions. Arura et al. [16] details the ambitious goals of the Paris Agreement, which include limiting the global average temperature increase to 1.5 °C by 2100 and achieving carbon neutrality by 2050. Given that the built environment contributes 38% of global energy-related CO₂ emissions, a fundamental transformation of the construction and building sectors is crucial to achieving these targets.

The building sector is currently grappling with a complex array of interconnected challenges spanning economic, environmental, technical, and social domains [17], which reinforces the need for integrated sustainability strategies aligned with the Sustainable Development Goals, which are defined by the United Nations within the 2030 Agenda [18], with SDG 9 (industry, innovation and infrastructure) and SDG 7 (affordable and clean energy) as the goals impacted by this work. These challenges are primarily driven by unprecedented global and regional climate change, demographic pressures, rapid urbanization, unsustainable resource utilization, and persistent socioeconomic disparities. Because of these multifaceted issues, there is an observed surge in electricity demand, which can be attributed to the intricate relationships between accelerated urban development, economic growth, and intensified construction activities [19]. This increased energy consumption is both a symptom and a driver of the sector’s challenges, creating a feedback loop that exacerbates existing problems. The interplay between these factors necessitates a holistic approach to research and policy-making, focusing on sustainable urban planning, energy-efficient technologies, and socially equitable development strategies to mitigate the building sector’s environmental impact while meeting the growing demands of an urbanizing world.

Previous works about scalable solutions for enhancing environmental sustainability based on the optimal size of the photovoltaic system coupled with battery storage [20,21] propose low-impact strategies for policy-making in the building sector. Other studies [22] acknowledge the potential solutions as adoption of renewable energy and electric vehicles but emphasize the need to address the intermittent nature of renewable energy generation. This intermittency, coupled with the unpredictable charging patterns of electric vehicles, as highlighted by [23], introduces complexities in ensuring a stable and reliable energy supply. Therefore, effective integration of these technologies requires strategies to mitigate the impact of their inherent variability on the energy grid. Chou and Nguyen [24], experimental research was focused on training predictive models using historical energy consumption data and weather patterns with the aim of predicting energy consumption one year in advance.

Previous research works have developed multi-objective optimization for improvements in various aspects, as [25], which, to get the final optimal solution in multi-objective optimization problems, used interactive methods and Pareto-dominated methods. The authors developed multi-objective optimization methods applied to environmental protection fields, for optimization objectives of energy saving, emissions reduction and cost reduction. This type of research work focused on optimization, process control and scheduling requires the interaction of multiple conflicting objectives (frequently imprecise due to uncontrollable factors). In these cases, to achieve optimal solutions, it is necessary to determine a set of points that identify that optimal point represented by the Pareto frontier.

The future and present of the sector has been identified by previous authors [26]: currently, the energy sector presents a large-scale distribution of energy, which means that information data growing exponentially is required to be handled. Consequently, the big data to be managed for decision-making is a thorny problem for traditional multi-objective optimization algorithms.

The optimization of energy consumption in buildings requires a multifaceted approach that considers various factors, including daylight utilization; ref. [27] have developed a multi-objective optimization algorithm aimed at minimizing energy consumption while maximizing daylight illuminance. This approach highlights the potential for achieving significant energy savings through integrated building design strategies [28], balancing energy savings with environmental and economic viability.

Furthermore, Mawson and Hughes [29] emphasizes the financial burden imposed on manufacturing companies by peak-load-dependent energy pricing. To mitigate these costs, can Duin and Geerlings [30] propose several strategies, including load shedding, peak sharing, equipment ramp-up procedures, and energy storage. These strategies offer the potential to reduce electricity bills by 10–30% by optimizing energy consumption patterns and reducing reliance on peak-demand periods.

One approach to address such design complexities is the use of optimization models. As ref. [31] suggests, these models offer a valuable framework for navigating multiple objectives and constraints, effectively guiding decision-making towards optimized design solutions. By incorporating factors such as energy efficiency, cost-effectiveness, and occupant comfort, optimization models can help achieve a balance between competing priorities.

The integration of Artificial Intelligence (AI) into the energy sector offers significant opportunities to improve efficiency, reliability, and sustainability. AI techniques—including big-data processing, advanced computation, and ML/DL algorithms—have been shown to support energy-efficiency goals and contribute to cleaner and more secure energy systems [32,33]. In the renewable-energy domain, AI enables enhanced infrastructure monitoring, improved operational security, and innovative market solutions [34].

In Spain, the national Artificial Intelligence Strategy [35] reflects a strong commitment to applying AI across the electricity sector, including decision-making support, environmental protection, and risk mitigation. AI is already being used to optimize the sizing and maintenance of solar and wind installations, improving system performance and operational efficiency. Complementing this strategy, the National Green Algorithms Programme (PNAV) [36], funded through the Next Generation EU initiative, promotes “Green by Design” AI to support environmental monitoring, resource efficiency, decarbonization, and circular-economy objectives. Together, these initiatives position Spain as a leader in environmentally sustainable AI development aligned with EU priorities.

The study aims to design a building materials factory that uses photovoltaic energy, based on sustainability criteria, identifying three key performance indicators (KPIs) for the manufacturing process: self-consumption, solar utilization and CO₂ emissions avoided being a stable combination of KPIs that robustly measure the environmental and economic potential of the photovoltaic installation. Furthermore, the study evaluates, through Pareto front analysis, the conflict between the proposed KPIs, identifying different types of facilities according to their greater environmental or economic potential. Through this innovative process to analyze and moons based on both performance and sustainability indicators, the present research proposes a method to guide the strategic decision for factory managers to size these installations.

Therefore, after outlining the framework, the present study assesses the specific case of photovoltaic systems as a sustainable solution advancing on the field of renewable energy integration in industrial settings by addressing critical gaps in prior research. In that sense, three key contributions can be remarked: (1) real-world data-driven analysis: unlike theoretical or generalized studies, this work is grounded in empirical data from an operational construction materials factory under Grupo Puma [37], including hourly energy consumption patterns, PV system parameters, and localized climatic conditions. By leveraging real-world data, the methodology ensures practical validation and directly applicable insights for industrial stakeholders. (2) Harmonizing sustainability and economic performance: while the existing literature often treats environmental and economic objectives as separate priorities, this study introduces a holistic framework using Pareto front analysis to quantify the trade-off between energy self-consumption (a sustainability metric) and solar utilization (an economic efficiency indicator). This dual-objective approach enables decision-makers to identify PV sizing strategies that balance decarbonization goals with financial viability. (3) Scalable and adaptable methodology: the proposed model adopts a modular structure—comprising consumption analysis, solar resource evaluation, parametric simulation, and multi-objective analysis—that is inherently scalable. This design allows seamless adaptation to other Grupo Puma facilities or similar industrial plants, regardless of geographic location or operational scale. The reproducibility of the proposal methodology not only broadens its applicability but also supports sector-wide standardization of sustainable energy practices, overcoming the fragmented approaches prevalent in current industrial strategies.

As indicated in the following sections, the present research proposes a stable trinomial of KPIs (self-consumption, solar utilization, and avoided CO₂ emissions) to robustly assess the environmental and economic performance of photovoltaic installations evaluated in the factory studied. The methodology, applied to Grupo Puma’s implement the model, uses real consumption data, executed photovoltaic installation projects, and climatological data from PVGIS that have been provided by the company on a real scale. Results will demonstrate that the factory achieves an optimal balance between self-consumption and solar utilization, as well as a substantial reduction in CO₂ emissions.

2. Experimental Methodology

The present research follows the experimental methodology illustrated in Figure 1. The specific inputs, variables, and output parameters integrated into the model are detailed in

Table 1. Model parameters.

Input	Variable	Output
PV module nominal power.	Number of PV modules	Solar utilization
PV module thermal loss coefficient	Tilt	Self-consumption
PV module nominal temperature	Azimuth	CO2 emissions avoided
PV module nominal irradiance
PV installation electrical efficiency
Irradiance
Temperature

.

Traditionally, the economic performance of photovoltaic (PV) installations is expressed through the payback period, while their environmental impact is measured in tons of CO₂ emissions avoided. However, these indicators are susceptible to temporal fluctuations that render them unreliable as long-term reference points for the entire lifespan of the installation:

(1)

Economic sensitivity to energy tariffs: Payback periods are intrinsically linked to the cost of electricity drawn from the grid and the compensation rates for surplus energy exported. The financial magnitude of both variables is dictated by a constantly evolving energy market [38], making long-term projections increasingly complex [39]. This volatility undermines the robustness of the payback period as a standalone indicator of economic potential.

(2)

Decarbonization of the electrical distribution system: Avoided CO₂ emissions are typically calculated using emission intensity ratios (e.g., tCO₂/kWh [40]) provided by the electrical grid. However, the progressive integration of cleaner energy sources is steadily reducing these values. Consequently, evaluating environmental impact based solely on avoided tonnage may lead to diminishing values over time, as they are heavily influenced by external decarbonization policies rather than the installation’s inherent performance.

This study aims to establish stable, long-term criteria for PV sizing based on sustainability. To achieve this, empirical data from an industrial facility in Southern Spain are utilized to validate the system model according to these pre-established parameters.

2.1. Identification of Key Performance Indicators of the System in the Case Study

Defining the specific KPIs that govern the sizing strategy is essential for establishing the model’s foundation. Given that traditional indicators depend on external factors, this study proposes the following environmental–economic KPIs for a long-term strategy:

(1)

Self-consumption: This metric quantifies the percentage of the factory’s energy demand met directly by the PV installation, which carries zero associated emissions. Independent of grid decarbonization trends, this value provides an accurate representation of the installation’s intrinsic environmental impact.

(2)

Solar utilization: This indicates the percentage of generated PV energy consumed on-site, with the remainder exported as surplus. Since the financial savings from self-consumption consistently outweigh those from surplus compensation, solar utilization reflects the installation’s economic potential before the application of fluctuating energy tariffs.

(3)

CO₂ emissions avoided: This is calculated by applying the grid’s emission intensity factor to the energy consumed on-site. By linking renewable energy usage directly to emissions displacement, this variable serves as a clear metric for climate change mitigation.

The development of the model to derive these decision values and their integration into a sustainable sizing strategy are detailed in the following sections.

2.2. System Modelling Description

Grupo Puma is a Spanish construction materials production company with international projection, being the main mortar manufacturer at national level with more than 20% market share and over 20 plants distributed across the country [37].

The following methodology (shown in Figure 2) for modelling energy consumption performed on one of Grupo Puma’s factories is intended to be a reproducible strategy for the rest of the facilities, obtained from the factory’s real consumption data, the photovoltaic installation projects executed (if any) and climatological data from PVGIS [41].

2.2.1. Factory Consumption Analysis

One of Grupo Puma’s factories was selected for the present analysis. To analyze its energy consumption, hourly electricity load data through 2023 was provided by the factory for this study. Figure 3 shows the statistical consumption distribution on working days and weekends. Production is concentrated within the 6:00 a.m. to 2:00 p.m. range, with power peaks of 110 kWh, with a base hourly consumption in the range of 10–20 kWh, as well as the work break on weekends, during which no consumption above the aforementioned base can be seen.

As for the seasonality of consumption throughout the year, Figure 4a shows a difference of up to 20% between the highest (July) and lowest (February) consumption months, with a greater consumption being observed in the second half of the year.

By analyzing the daily consumption curve in the highest and lowest consumption months of the year, according to Figure 4b, two main differences are observed:

(1)

Consumption within the 6:00 a.m. to 2:00 p.m. range, which shows the fluctuation of the factory’s production in each month. This difference is not necessarily related to the volume of production but could also be due to the type of product manufactured and, therefore, the energy consumption associated with each process.

(2)

Consumption within the 3:00 p.m. to 6:00 p.m. range, with a relatively stable gap of approximately 7 kW, which is attributed to air-conditioning equipment operating during office working hours.

As the highest energy consumption is concentrated in the photovoltaic generation time frame, such installations have a promising potential in the factory under study.

2.2.2. Solar Resource Analysis

Photovoltaic generation depends essentially on the availability of energy obtained by solar panels through solar radiation. The solar resource, expressed in terms of power: irradiance, W/m² or energy: radiation, Wh/m², consists of three components: Direct ($G_D$): as a consequence of the phenomenon of absorption of directly received radiation; Diffuse ($G_d$): as a consequence of the phenomenon of diffusion of radiation after its reflection through clouds and particles in the air and Albedo ($G_a$): as a consequence of the reflection phenomenon, it is obtained by the reflection of radiation on the land surface. Total irradiance value ($G_T$) for each hour of the year is obtained from the climatological data obtained in PVGIS for 2023 at the location of the factory under study.

In addition to the irradiance distribution throughout the day shown in Figure 5a, a seasonal variation in this value is noteworthy, as can be seen in Figure 5b, where difference over 200 W/m² is reached between the months with the highest (June) and lowest (January) irradiance values.

2.2.3. Ambient Temperature and Module Temperature Analysis

Photovoltaic phenomenon is also affected by ambient temperature, reducing its performance at higher temperatures. Previous works affirm that ambient temperature reduces the efficiency by approximately 0.4–0.5% per additional degree Celsius., which limits the productivity of systems in hotter climates and should be considered when planning and optimizing solar installations in high-temperature regions [42]. Figure 6 shows the hourly distribution of temperatures throughout the whole year at the factory location, showing a hot climate in which the thermal impact on the installation cannot be dismissed.

To evaluate the effect of ambient temperature on the photovoltaic modules, the module temperature, T_mod is calculated according to Equation (1):

$$T_{mod}=T_{amb}+\left(T_{ref}-20\right)\times G_T/800$$

(1)

where $T_{ref}$ is the reference temperature of the photovoltaic module. From this calculation, Figure 7 shows how average module temperatures are substantially higher, and this difference is accentuated during summer, which are also those with the highest irradiance.

This calculation implies that average module temperatures are substantially higher than the ambient temperature, and this difference is accentuated during summer, which are also those months with the highest irradiance.

2.2.4. Photovoltaic Module Analysis

Choice of photovoltaic module involves different system perspectives, such as the electrical circuit, efficiency or surface area covered. In this study, since the plant currently has a photovoltaic installation, only the used module was modelled with the following parameters:

• Nominal power: 400 W.
• Thermal loss coefficient: 0.0037 °C⁻¹.
• Nominal temperature: 25 °C.
• Nominal irradiance: 1000 W/m².

2.2.5. System Performance Losses

In this study, three possible causes of system performance losses are considered: thermal efficiency, ${\eta }_{thermal}$, mounting method efficiency, ${\eta }_{mount}$, and electrical efficiency, ${\eta }_{elect}$ [43].

About thermal efficiency, ${\eta }_{thermal}$, system performance is compromised by temperatures above the nominal temperature of the module. The performance due to thermal causes is calculated as shown in Equation (2):

$${\eta }_{thermal}=\left\{\begin{array}{cc}1& , T_{mod}\le T_{ref}\\ 1-{\alpha }_{thermal}·\left(T_{mod}-T_{ref}\right)& , T_{mod}>T_{ref}\end{array}\right.$$

(2)

The hourly fluctuation of the thermal losses throughout the day is accentuated in hot seasons, frequently exceeding 2% losses, and it is shown in Figure 8.

The second factor of system performance losses considered is the mounting method efficiency, ${\eta }_{mount}$ as azimuth (deviation from the south orientation) and tilt (deviation from the horizontal plane) which affect the performance of the system, as shown in Equation (3).

$${\eta }_{mount}=\left\{\begin{array}{cc}1-1.2\times {10}^{-3}\times \left|{\beta }_{optimal}-\beta \right|& , \beta \le 15\\ 1-1.2\times {10}^{-3}\times \left|{\beta }_{optimal}-\beta \right|+\left({\alpha }^2\times 3.5\times {10}^{-5}\right)& , \beta >15\end{array}\right.$$

(3)

Finally, the last factor considered on system performance losses is electrical efficiency, ${\eta }_{elect}$. The phenomena of conduction and conversion of electrical energy from its generation on DC until it reaches the AC loads of the installation greatly affect the overall system efficiency. In this study, an efficiency of 0.9 will be attributed to the installation due to the losses caused in the DC conduction, the DC/AC conversion, and the AC conduction. This assumption of 10% of electrical losses in energy performance is justified by:

• 2% from wire conduction [44].
• 2% from the inverter [45].
• 4% from soiling [46].
• 2% from I-V curve mismatch [47].

2.2.6. Global Photovoltaic Performance Analysis

After detailing system components and the environmental and installation causes that affect its performance, all these variables combined determine the photovoltaic AC power according to Equation (4).

$$P_{PV}=P_p·G_T·{\eta }_{thermal}·{\eta }_{mount}·{\eta }_{elect}/G_{ref}$$

(4)

where $P_p$ represents the peak photovoltaic nominal DC power, because of multiplying the number of modules installed by its individual nominal power capacity. It can be observed that, depending on the module nominal irradiance, the value of $G_T$ will have a greater impact on final power generation. Figure 9 shows the PV generation hourly obtained per kWp installed.

2.2.7. Model Evaluation Variables

Based on the data obtained from the model, the following three variables are determined to evaluate the performance of the system: self-consumption, solar utilization and CO₂ emissions avoided.

Firstly, self-consumption references the factory’s energy consumption that is covered by photovoltaic generation. Its calculation method is presented as in Equation 5, depending on whether the factory’s demand is completely covered.

SelfCom variable is one of the decision variables of the proposed strategy, as it represents the PV installation’s environmental potential due to the factory’s dependency on renewable sources.

$$SelfCom=\left\{\begin{array}{c}1 , P_{PV}>C\\ P_{PV}/C , P_{PV}\le C\end{array}\right.$$

(5)

The second factor is solar utilization. In this case, Equation (6) shows the calculation of this variable, which reflects the proportion of PV generation that is dedicated to self-consumption, as opposed to being transferred as energy excess to the grid.

$$SolarUtil=\left\{\begin{array}{c}C/P_{PV} , P_{PV}>C\\ 1 , P_{PV}\le C\end{array}\right.$$

(6)

SolarUtil is the second decision variable in the proposed strategy, representing the economic potential of the installation in terms of energy profitability, according to its use.

Finally, the third variable is CO₂ emissions avoided. Taking as a reference the grid emissions value of 178 g CO₂/kWh [48], the calculation of avoided emissions based on the factory’s self-consumption is established proportionally. This EU average grid emission factor is used due to the availability of established projections at European level, which are not yet provided for Spain.

Despite not being taken as a reference value for environmental impact in the decision strategy, given the fluctuation of the value of tCO₂/kwh, it is worth specifying in absolute terms the contribution of the installation to the factory in terms of sustainability.

2.2.8. Methodological Validation Using PVGIS

The robustness of the photovoltaic modelling approach was ensured by validating the step-by-step equations against methodologies widely adopted in the recent literature. The model relies on irradiance and temperature inputs obtained from PVGIS, whose satellite-derived datasets and performance algorithms have been extensively validated. For instance, ref. [49] reports that “RETScreen and PVGIS COSMO provided the best results during the different months of the year” highlighting the reliability of PVGIS as a source of meteorological data for photovoltaic assessments.

Following the approach commonly used in recent studies, photovoltaic generation was estimated by applying standard physical equations to PVGIS inputs, rather than by benchmarking against a specific PVGIS power–output curve. Works published [50,51,52] demonstrate that this combination—PVGIS irradiance and temperature data together with established PV performance equations—yields accurate and consistent results across diverse contexts. The strong consensus in the literature regarding the validity of this methodology supports the robustness of the modelling framework adopted in this study.

2.3. Simulation Based on the Model

Once the model has been defined, it is indicated that the simulation is then carried out for different values of two input variables (nominal power of the installation and inclination of the modules), highlighting the gathering of real data for the model (real consumption of the factory, project execution of the current photovoltaic installation and PVGIS climatological data).

The simulation includes the calculation of self-consumption, solar utilization and avoided CO₂ emissions for values from 0 to 200 peak kW installed, in increments of 0.4 kW, and 0° to 45° module tilt, in increments of 1°. The proposed model was developed using Python 3.12.3 programming environment Spyder, running on an HP Laptop 15s-fq1xxx computer with Intel i7 processor and 12 GB of RAM.

3. Results and Discussion

Once the model has been simulated for a total of 23,000 combinations of module tilt and installed PV power, the established system evaluation variables are analyzed, and the sizing strategy is presented. A partial comparison using a single monitored month was considered, but it was discarded because it would not provide a representative validation due to seasonal variability. Full-year monitored PV data were not yet available at the time of model development.

Before analyzing the results, it should be highlighted that the photovoltaic model relies on a validated combination of PVGIS meteorological data and standard PV performance equations, ensuring the robustness of the simulated indicators.

This study is based on a single real scale industrial facility, and the results reflect the specific operational conditions of the selected factory. Due to confidentiality constraints, comparable datasets from other industrial plants are not publicly available, which limits cross factory validation at this stage. The proposed modelling framework, however, has been designed to be scalable, and future work will extend the analysis to additional factories to assess generalizability and sensitivity to different consumption patterns, energy price scenarios, and grid decarbonization trajectories.

3.1. Consumption and Photovoltaic Generation Curves Comparison

Figure 10a shows the factory’s demand curve comparison during the highest consumption month (July), combined with different photovoltaic generation curves according to installed power. It is observed that increasing values of installed power results in higher factory self-consumption, although this increment becomes progressively decreasing.

Figure 10b shows the comparison for the lowest consumption month at the factory (February), and it is possible to identify an aspect of improvement in economic and environmental terms in the installation: by delaying production start for two hours during this season, energy demand would be covered to a greater extent by photovoltaic generation, which would substantially increase the factory’s self-consumption and, therefore, reduce CO₂ emissions and reduce the cost of energy.

3.2. Self-Consumption Analysis

Figure 11a shows self-consumption curve by means of the simulation input variables. As previously mentioned, it is observed how self-consumption increments decrease as the installed power increases. Module tilt, although not especially significant in comparison to installed power, has a greater impact on self-consumption for greater PV plants installed. This limited sensitivity is consistent with previous studies showing that, at mid-latitudes, annual PV yield varies only marginally for tilt angles between 0° and 45° due to the combined effect of diffuse irradiance and seasonal solar altitude [53].

3.3. CO₂ Avoided Emissions Analysis

The proportional dependence between self-consumption already established in this paper methodology implies similar tendencies for both variables. As shown in Figure 11b, emissions avoidance is decreasingly increased by means of installed power, depending on the reference value of distribution grid emissions.

3.4. Solar Utilization Analysis

In contrast with the study of the factory’s self-consumption, it can be observed in Figure 12 that solar utilization decreases in accordance with higher values of installed power: as photovoltaic generation is above the factory’s consumption, excess energy is delivered to the grid, reducing the economic profitability of the energy produced. Figure 12 is based on previous works [54] which estimated optimal tilt angles for photovoltaic panels worldwide. Studies such as [55] demonstrate that in self-consumption systems, deviations of up to ±15° from the theoretical optimum typically have impacts of less than 2–3% on final profitability.

The value approaches linear behaviour from 75 kWp, and as observed for the case of self-consumption, the effect of the module tilt also increases with the installed power.

3.5. Pareto Front for Sustainability-Based Sizing Decision Strategy

To establish a comprehensive sizing strategy, self-consumption and solar utilization were selected as long-term sustainability criteria. These metrics inherently compete as installed power capacity increases, reflecting the trade-off between economic and environmental impacts. To evaluate the set of possible solutions, a Pareto front representation of these two decision variables is employed to illustrate the economic and environmental potential of various PV configurations.

The construction of a Pareto front provides a systematic framework for analyzing the relationship between multiple conflicting objectives. This process involves defining objectives and decision variables, generating potential solutions, and evaluating the performance values for each objective. Solutions undergo a comparative analysis based on dominance: a solution is classified as “dominated” and subsequently discarded if another solution surpasses it in at least one objective without performing worse in any other. The resulting collection of non-dominated solutions constitutes the Pareto front. As visualized in Figure 13, this front defines a trade-off curve of the most efficient compromises, facilitating informed decision-making based on strategic priorities. In this specific context, the example illustrates a Pareto front for solutions aimed at minimizing both objectives (F1 and F2).

• Figure 14 illustrates the conflict between these two variables, where one objective typically improves at the expense of the other. Based on the Pareto front analysis, three distinct regions have been identified:
• Region 1: Economic performance zone: for installations with up to 20% self-consumption, the system achieves its highest solar utilization values (50–70%). While this range yields the highest economic performance, its environmental impact remains relatively modest.
• Region 2: Intermediate zone: within the 20–40% self-consumption range, an approximately linear variation occurs between the intermediate values of both decision variables. Notably, increases in self-consumption of up to 20% can be achieved at a cost of only 10% in solar utilization. This implies that in this region, the factory’s sustainability can be substantially improved with only minor reductions in economic efficiency.
• Region 3: Higher sustainability zone: beyond 40% self-consumption, further increases require significant decreases in solar utilization. This region is primarily restricted to facilities willing to prioritize maximum sustainability over the economic yield of their PV installation.

Figure 14 further highlights the current positioning of the Grupo Puma factory relative to its consumption data. Its actual PV installation is located on the boundary between the intermediate and high sustainability zones. Consequently, the data reveals that the factory’s PV system has been sized to prioritize sustainable capability without incurring disproportionate losses in economic performance.

4. Conclusions

This study, conducted in collaboration with a real industrial operator in Southern Spain, enhances energy sustainability by modelling a construction materials factory through a photovoltaic (PV) sizing strategy based on three key performance indicators (KPIs), facilitating the derivation of several key findings:

(1)

Sustainability plans frequently lack a comprehensive approach to renewable energy; while they often address ISO standards and life cycle strategies, they provide limited guidance regarding practical implementation or performance evaluation.

(2)

Photovoltaic installations represent a widespread and effective solution for incorporating renewable energy into industrial production processes. However, conventional KPIs for such studies (specifically CO₂ emissions and payback periods) lack long-term consistency as they are subject to fluctuations in the energy market and ongoing grid decarbonization. In this context, self-consumption, solar utilization, and avoided CO₂ emissions are proposed as a stable trinomial of KPIs to robustly measure both the environmental and economic potential of a PV installation. The results demonstrate that Grupo Puma’s current installation achieves an optimal balance, reaching self-consumption levels near 39% and solar utilization of approximately 40%, thereby proportionally reducing CO₂ emissions into the atmosphere.

(3)

Through Pareto front analysis, which illustrates the conflict between the proposed KPIs, it is possible to identify various types of facilities based on whether their potential is primarily environmental or economic. A central contribution of this work has been the evaluation of conflicting and independent objectives to find a balance between two often contrasting priorities: economy and sustainability. In this case, three distinct regions were defined: an economic performance zone (up to 20% self-consumption with high solar utilization of 50–70%), an intermediate zone (20–40% self-consumption), and a high sustainability zone (exceeding 40% self-consumption). The study reveals that within the intermediate zone, it is possible to increase self-consumption by up to 20% at the cost of reducing solar utilization by only 10%, demonstrating that sustainability can be significantly improved with minor losses in economic efficiency. Ultimately, this approach allows for the evaluation of existing PV installations according to their environmental performance, as well as the sizing of new systems based on these integrated sustainability–economic criteria.

Based on these findings, this work provides a solid foundation for future research at the PUMA factory. Incorporating energy storage, product-specific data, and dynamic energy tariffs would allow for a more detailed assessment of photovoltaic potential; furthermore, optimization techniques such as genetic algorithms are recommended to identify optimal solution.

The modelling framework, built upon PVGIS meteorological inputs and standard PV performance equations validated in the recent literature, offers a robust foundation for the photovoltaic estimates presented. Future access to full-year monitored PV data will allow a dedicated validation study to further consolidate these results.

Finally, this study highlights the critical importance of using real operational data from industrial operators to improve sustainability assessments and simulations. By leveraging actual production data, it provides an actionable framework showing that strategic energy management and renewable energy adoption can address climate challenges while maintaining economic performance. Using this set of indicators, the analysis shows that Grupo Puma’s installation achieves an optimal balance, with approximately 39% self-consumption, 40% solar utilization, and substantial avoided CO₂ emissions. The Pareto front analysis further indicates that self-consumption could be increased by up to 20% with only a ~10% reduction in solar utilization. Together, these results provide a clear recommendation for Grupo PUMA, offering actionable guidance to support industrial decision-making by prioritizing higher self-consumption to enhance sustainability performance while maintaining acceptable economic efficiency.