Probabilistic Assessment of Solar-Based Hydrogen Production Using PVGIS, Metalog Distributions, and LCOH Modeling

Abstract

The transition toward low-carbon energy systems requires reliable tools for assessing renewable-based hydrogen production under real-world climatic and economic conditions. This study presents a novel probabilistic framework integrating the following three complementary elements: (1) a Photovoltaic Geographical Information System (PVGIS) for high-resolution, location-specific solar energy data; (2) Metalog probability distributions for advanced modeling of variability and uncertainty in photovoltaic (PV) energy generation; and (3) Levelized Cost of Hydrogen (LCOH) calculations to evaluate the economic viability of hydrogen production systems. The methodology is applied to three diverse European locations—Lublin (Poland), Budapest (Hungary), and Malaga (Spain)—to demonstrate regional differences in hydrogen production potential. The results indicate annual PV energy yields of 108.3 MWh, 124.6 MWh, and 170.95 MWh, respectively, which translate into LCOH values of EUR 9.67/kg (Poland), EUR 8.40/kg (Hungary), and EUR 6.13/kg (Spain). The probabilistic analysis reveals seasonal production risks and quantifies the probability of achieving specific monthly energy thresholds, providing critical insights for designing systems with continuous hydrogen output. This combined use of a PVGIS, Metalog, and LCOH calculations offers a unique decision-support tool for investors, policymakers, and SMEs planning green hydrogen projects. The proposed methodology is scalable and adaptable to other renewable energy systems, enabling informed investment decisions and improved regional energy transition strategies.

1. Introduction

In recent months, in European Union countries and around the world, the production of green hydrogen has become a priority [1,2]. Very large financial resources have been allocated to the development and implementation of technologies for the production [3], storage [4,5], transport [6], and use of green hydrogen in the transport [7] and chemical production sectors. These activities are the consequence of zero hydrogen emissions. Using hydrogen as a fuel or substrate for production does not generate any harmful emissions. The use of hydrogen in combustion or slow chemical reactions has no carbon footprint. Moreover, hydrogen has been recognized as a medium suitable for the long-term storage of large amounts of energy [8]. Therefore, hydrogen can be produced from excess electricity produced by renewable energy sources (RESs) and then used in hydrogen fuel cells or industrial production processes [9,10].

The production and use of hydrogen has been recognized as a solution to problems related to the combustion of fossil fuels and the accompanying emissions of carbon dioxide and other regulated and unregulated exhaust gas components into the atmosphere [11,12,13,14,15]. The use of hydrogen as a fuel for combustion engines is the subject of many scientific studies [16,17,18,19,20]. In the face of diminishing reserves of conventional fuel sources such as coal, oil, and natural gas, the global community is compelled to explore alternative energy sources. This is exemplified in the context of transport by plant-based fuels, which are referred to as biofuel [21,22,23]. A notable development in this field is the increased focus on hydrotreated vegetable oil (HVO) [24,25]. In addition, various gaseous fuels are being studied, such as compressed natural gas (CNG) in many applications [26,27,28], liquefied natural gas (LNG) [29,30], liquefied petroleum gas (LPG), which is popular in many European countries [31,32,33], natural gas (NG) [34,35], and other alternative fuels [36,37,38]. The fuels mentioned can power individual motor vehicles [31,39], as well as fleets of trucks [40], city buses for public transport [41], and agricultural tractors [27]. The use of alternative fuels serves as a means to facilitate the transition of the transport sector towards lower-emission energy sources for various means of transport, and ultimately to electric vehicles, which are characterized by zero emission at the point of use.

In the first three decades of the 21st century, there has been a major increase in the production capacity of electricity produced from RESs around the world and in Europe [42]. These RESs usually take the form of photovoltaic systems and wind systems [43]. The former produce electricity from solar radiation reaching our planet. The latter utilize the kinetic energy of winds blowing on Earth. Both of these energy sources are inexhaustible. The production of electricity from both of these sources is highly variable. For instance, the generation of electricity by photovoltaic systems results from the variability of sunlight during the day and its lack at night, as well as the changing seasons [44]. Electricity production from wind turbines is also highly variable [45]. The variability of the amount of energy produced from renewable energy sources causes problems with energy balancing in energy networks [46], which require large and cheap energy storage facilities capable of storing large amounts of electricity for longer periods of time. There are many technologies in this area. The simplest of them include pumped storage power plants. Another solution may be large stationary energy storage systems based on lithium-ion batteries [47]. However, they are characterized by high costs and a limited number of charging and discharging cycles, which results in a limited operating time. Hydrogen is another solution for energy storage needs, however, there are still many technological challenges related to the effective production of hydrogen, its safe storage and transportation, and its use in transport and industrial production. Depending on the source it was produced from, hydrogen is color-coded [48]. For example, white hydrogen comes from natural geological sources and gray hydrogen is produced by the steam reforming of natural gas. Hydrogen produced using electricity from renewable energy sources is called green hydrogen [49].

In the scientific community, hydrogen has been recognized as a medium perfect for storing and transporting large amounts of energy over a long period of time [50]. Firstly, the production of hydrogen using water electrolysis methods is now a very well-known process that can be widely applied [51]. The market currently offers electrolyzers in PEM [52,53], AEM [54,55], SOFC [56,57], and AFC technologies [58]. Scientists are currently also developing innovative photoelectrolytic [59], photoreforming [60], and thermophotocatalytic methods for hydrogen production, which may be an alternative to electrolyzers [61]. To generate 1 kg of hydrogen through electrolysis, around 50 kWh of electricity is required, while the energy content of that kilogram of hydrogen is about 33 kWh.

Secondly, hydrogen storage processes in both the liquid (cryogenic) and compressed phases have also been well researched and developed, and can be widely adopted [62,63]. In industrial practice, hydrogen is transmitted through gas pipelines in compressed form and transported in pressure tanks at a pressure of 350 or 700 bar. For this purpose, steel or composite tanks are used, which are much lighter than steel ones [64]. Composite tanks also constitute mobile hydrogen storage for hydrogen vehicles [65,66].

Thirdly, electricity and heat can be easily recovered from hydrogen using hydrogen fuel cells. Fuel cells are currently built using many technologies and have stationary and mobile applications [67]. They integrate perfectly with the electric drives of passenger cars and buses [68,69].

Therefore, at the moment, within the hydrogen technology chain, also referred to as the so-called hydrogen economy, the only missing element is a stable and cheap energy source to power hydrogen electrolyzers [70]. Large hydrogen plants can be powered by photovoltaic systems, wind farms, and a mix of these two RESs [71,72,73]. Many scientists believe that low-emission hydrogen produced from RESs is the only practical medium that can replace fossil fuels in many industries and, thus, contribute to reducing carbon dioxide emissions [74,75].

The novelty of this paper lies in the integration of three complementary tools and methodologies—a Photovoltaic Geographical Information System (PVGIS), Metalog probability distributions, and Levelized Cost of Hydrogen (LCOH) modeling—into a single analytical framework for assessing green hydrogen production potential. While PVGISs are widely recognized for providing reliable, location-specific estimates of solar energy yield, their combination with the flexible and mathematically robust Metalog distributions enables a detailed quantification of energy production variability, risk, and uncertainty, which is often neglected in traditional studies. By adding a comprehensive LCOH analysis, this study creates a unique bridge between probabilistic modeling and practical economic assessment, allowing decision makers to evaluate not only energy yields, but also investment feasibility and hydrogen cost projections in real-world scenarios.

To the best of our knowledge, this is the first publication that systematically integrates these three methodologies to compare hydrogen production potential across geographically and climatically diverse regions of Europe. Existing studies often focus on deterministic or averaged results, providing only limited insights into seasonal risks, probabilistic thresholds, and the financial implications of variability in renewable energy output. The proposed framework overcomes this limitation by explicitly modeling uncertainty, presenting sensitivity analyses, and delivering a transparent, replicable methodology that can be applied to both micro-installations and larger-scale renewable hydrogen systems.

From a practical standpoint, this approach offers significant value for small- and medium-sized enterprises (SMEs), local energy developers, and policymakers. By leveraging freely available PVGIS data, an open-formula statistical distribution family (Metalog), and standard economic indicators such as LCOH, the study provides a low-cost, scalable decision-support tool that empowers stakeholders to make evidence-based decisions about renewable energy and hydrogen investments. The methodology is designed to be accessible and adaptable, enabling rapid evaluations of different scenarios, investment scales, and technological configurations without requiring expensive proprietary software or large datasets.

This integrated perspective is particularly relevant in the context of the European Green Deal and national decarbonization strategies, which increasingly emphasize localized renewable energy solutions and low-emission hydrogen as a cornerstone of the energy transition. By combining advanced probabilistic modeling with cost analysis, this work contributes to bridging the gap between academic research and industry needs. The insights offered are of a practical nature and are intended to support energy planners, technology providers, and entrepreneurs in accelerating the adoption of clean hydrogen technologies.

2. Building of New Energy Generating Capacity for Hydrogen Production

Building new energy capacity in Europe for low-emission hydrogen primarily means developing renewable energy sources (RESs) and electrolysis technologies [76]. This means investing in wind farms, solar farms, and nuclear power plants that will provide clean energy for the production of low-emission hydrogen. A key goal is to reduce CO₂ emissions and replace grey hydrogen (from fossil fuels) with green or low-emission hydrogen. New infrastructure also includes the construction of electrolyzers that split water into hydrogen and oxygen using electricity from RESs. The development of these technologies is crucial for the decarbonization of industry, transport, and energy. European countries such as Germany, France, and The Netherlands are already investing billions of euros in hydrogen as part of the energy transition. This new capacity will help reduce Europe’s dependence on imported fossil fuels. Low-emission hydrogen can support grid stability by storing surplus energy from RESs. However, the development of this sector requires regulatory and financial support, including subsidies and incentives [77]. The end result will be a more sustainable and competitive economy based on clean energy. This topic is currently very relevant due to the uncertainty occurring in the fossil fuel market.

The authors compare the possibility of producing low-emission hydrogen in three European countries using only energy from ground-mounted photovoltaic systems with a peak power of 100 kWp. This is already a significant size for a photovoltaic system, sufficient to produce hundreds of kilograms of hydrogen per month. However, using only one RES from photovoltaics involves the need to store surplus energy produced during the day to power electrolysis processes at night. Adding a second RES in the form of wind turbines to the photovoltaic system is a step towards achieving a more balanced energy mix. However, a major limitation concerns financing when beginning the construction of a ground-mounted wind turbine, which many micro-, small-, and medium-sized companies cannot afford. Investments in the production of low-emission hydrogen from only photovoltaic systems are supported by decreasing the price of energy storage systems (ESSs).

An important regulatory dimension of renewable hydrogen production is compliance with the EU’s RFNBO (Renewable Fuels of Non-Biological Origin) certification framework, which imposes strict geographic and temporal correlation requirements between renewable energy generation and electrolyzer operation. Under RED III, these rules are being progressively tightened: hydrogen must be demonstrably produced using electricity from newly built or additional renewable assets located within defined geographical boundaries, and by 2030, electrolyzer operation must match renewable electricity generation on an hourly basis. These criteria are designed to ensure that hydrogen production contributes directly to decarbonization rather than relying on generic grid electricity. Such requirements have direct implications for system design, emphasizing the need for co-located PV–wind systems, smart dispatch strategies, and adequate hydrogen storage to bridge production gaps while maintaining certification compliance. The probabilistic modeling framework presented in this study offers a transparent and flexible approach for evaluating these regulatory constraints, supporting developers and policymakers in designing economically viable and regulation-compliant hydrogen production projects.

3. Materials and Methods

In this study, the authors use the Metalog family of probability distributions, which was developed by Tom Keelin in 2016 as a flexible alternative to classical probability distributions [78]. It is based on the expansion of the quantile function into a series, thereby enabling adjustment to empirical data without the necessity for assumptions regarding the shape of the distribution. The Metalog family of probability distributions allows for modeling one-sided, two-sided, and arbitrary-tailed distributions, including asymmetric and multimodal distributions [79]. Their parameters can be easily estimated using linear regression, which makes them particularly useful in data analysis. Their main applications include risk modeling, forecasting in economics, engineering, and social sciences. Compared to traditional distributions, Metalog better represents complex empirical data without the need for rigid theoretical assumptions. It can be used for analyzing large data sets, e.g., in machine learning or Monte Carlo analysis. Its flexibility makes it popular in modeling uncertainty and probabilistic decision making. Due to its open formula, it can be easily implemented in various computing environments such as Python, R, and Excel. GeNIe 5.0.4722 Academic software has a built-in family of Metalog probability distributions [80].

Metalog is becoming an increasingly popular tool in the field of statistical and probabilistic analysis [81]. The authors used the Metalog probability distribution family to calculate the probability of energy production by photovoltaic carports and to assess the technical condition of cells in battery packs of hybrid vehicles. In both cases, the Probability Density Function (PDF) was characterized by bimodality. This was found as an intriguing physical explanation.

4. Results

4.1. Characteristics of Energy Production from Photovoltaic Systems in Various European Countries

4.1.1. Characteristics of Energy Production from Photovoltaic Systems in Poland (Lublin)

A very important element of initial investment is having access to reliable data on power generation from photovoltaic systems in different countries. In this article, the authors used data from the Photovoltaic Geographical Information System (PVGIS) version 5.3 [82]. This is an online tool developed by the Joint Research Centre (JRC) of the European Commission (see Figure 1). It is used to assess the solar energy potential and efficiency of photovoltaic systems around the world. It allows users to analyze insolation, optimal panel tilt angle, and expected energy production for different locations. The PVGIS uses satellite and meteorological data, which allows for accurate forecasts in different climatic conditions. It supports various photovoltaic technologies, including stand-alone and building-integrated systems. The tool is useful for investors, scientists, and engineers planning PV installations. It offers functions for analyzing the impact of shading and system losses on the efficiency of energy production. The PVGIS also provides historical data, enabling the long-term assessment of solar conditions. It can be used for planning both small home installations and large solar farms. Its openness and accessibility make it a valuable tool supporting the development of renewable energy.

The amounts of monthly energy production by a photovoltaic system with a peak power of 100 kWp located the city of Lublin, Poland, are shown in Figure 2.

The monthly energy production data were digitally exported and analyzed with the GeNIe 5.0 Academic software. Both basic and advanced statistical computations were performed on the collected dataset. The minimum value of energy produced monthly was 2.83784 MWh, the maximum value was 13.58475 MWh, and the average value of energy produced was 9.02614 MWh, with a standard deviation of 4.20674 MWh. These data show that electricity production in Polish geographical conditions is characterized by a high variability due to the changing seasons. The Metalog distribution family enables advanced statistical analysis, including precise quantile estimation, as shown in

Table 1. Quantile parameters.

Probability	Energy Production [MWh]
0.05	2.837840080261
0.25	5.273059844971
0.5	10.72251987457
0.75	13.08139038086
0.95	13.58475017548

.

The GeNIe 4.1 Academic software makes it possible to calculate the Cumulative Distribution Function and the Probability Density Function for different k coefficients (Figure 3). The Probability Density Function graph indicates that high probability values are observed for both low and high monthly energy production levels. This indicates a strong influence of the seasons on the intensity of solar radiation and, therefore, on the amount of energy produced in Polish geographical and climatic conditions.

The subsequent stage of analysis involved extracting information from the knowledge base. Probabilities were calculated for monthly energy outputs of 5, 10, and 15 MWh. To obtain this information, the following query was posed: “What is the probability that a 100 kWp photovoltaic installation located in Lublin, Poland, will produce 5 MWh of electricity or less in a given month?” The system’s response was 0.25, meaning the probability of generating more than 5 MWh was 1 − 0.25 = 0.75. Similar queries were formulated for monthly outputs of 10 MWh and 15 MWh. This methodology, based on the Metalog distribution family, demonstrates its usefulness for simulating various photovoltaic energy production strategies to meet the electricity demands of electrolyzers for specific hydrogen generation targets. The computed probabilities are shown in

Table 2. Probability of energy output from a 100 kWp photovoltaic system situated in Poland.

Energy [MWh]	Probability ≤	Probability >
5	0.25	0.75
10	0.5	0.5
15	1	0

. The results clearly indicate that, under Polish geographical and climatic conditions, a 100 kWp system cannot achieve a monthly production level of 15 MWh.

4.1.2. Characteristics of Energy Production from Photovoltaic Systems in Hungary (Budapest)

Figure 4 presents the monthly energy production levels of a 100 kWp photovoltaic installation located in Budapest, Hungary.

Basic and advanced statistical analyses were performed on these data. The minimum recorded monthly energy production was 4.54527 MWh, while the maximum reached 14.47590 MWh. The mean monthly output was 10.38650 MWh, with a standard deviation of 3.68298 MWh. Both the minimum, maximum, and average values were higher in Hungary compared to Poland, while the standard deviation remained similar in both cases. This indicates that electricity generation in Hungary also showed strong seasonal variability, much like in Poland. However, the total annual energy output from a system of the same peak capacity was significantly higher, amounting to 124.6385 MWh in Hungary versus 108.3136 MWh in Poland. Detailed statistical measures of energy production are summarized in

Table 3. Quantile parameters.

Probability	Energy Production
0.05	4.545269966125
0.25	7.201940059662
0.5	11.66884040833
0.75	13.84545993805
0.95	14.47589969635

.

Likewise, with the use of GeNIe 4.1 Academic software, the Cumulative Distribution Function and Probability Density Function were generated for different k coefficients (Figure 5). The Probability Density Function plot reveals that the distribution of probability densities differed from that observed in Poland. This indicates a weaker impact of the seasons on the intensity of solar radiation and, therefore, on the amount of energy produced in Hungarian geographical and climatic conditions compared to Polish ones.

Following the same approach as for estimating the probability of monthly energy production in Poland, the knowledge base was queried regarding monthly generation levels in Hungary. The calculated probabilities are summarized in

Table 4. Probability of the amount of energy produced by a 100 kWp photovoltaic installation located in Hungary.

Energy [MWh]	Probability ≤	Probability >
5	0.0833	0.9167
10	0.4166	0.5834
15	1	0

. The results indicate that, under Hungarian geographical and climatic conditions—similar to those in Poland—a 100 kWp photovoltaic system cannot achieve a monthly output of 15 MWh.

4.1.3. Characteristics of Energy Production from Photovoltaic Systems in Spain (City of Malaga)

Figure 6 illustrates the monthly energy generation of a 100 kWp photovoltaic installation situated in Malaga, Spain.

Both basic and advanced statistical analyses were performed for this dataset. The lowest recorded monthly energy output was 11.35140 MWh, while the highest reached 16.78140 MWh. The mean monthly production amounted to 14.24611 MWh, with a standard deviation of 2.03659 MWh. Compared to Poland and Hungary, the minimum, maximum, and average values were significantly higher, while the standard deviation was more than twice as low as that in the Eastern European countries. This indicates that electricity generation in Spain is subject to much lower seasonal variation, with consistently abundant sunlight throughout the year. Moreover, the total annual production from a 100 kWp system in Spain far exceeded that of Hungary and Poland, reaching 170.9533 MWh compared to 124.6385 MWh and 108.3136 MWh, respectively. A detailed summary of these statistical findings is provided in

Table 5. Quantile parameters.

Probability	Energy Production
0.05	11.35138988495
0.25	12.17833995819
0.5	14.92626953125
0.75	16.34178924561
0.95	16.78140068054

.

Once again, the GeNIe 4.1 Academic software was used to generate the Cumulative Distribution Function and Probability Density Function for different k coefficients (Figure 7). The Probability Density Function plot demonstrates that the distribution of probability densities differed from that observed in both Poland and Hungary. This indicates a very weak impact of the seasons on the intensity of solar radiation in Spain and, therefore, on the amount of energy produced in Spanish geographical and climatic conditions compared to Polish and Hungarian ones. Natural energy sources, such as solar energy, may also encounter certain limitations, especially when heavy rainfall occurs, similar to that during the rainy season [83].

Using the same method applied for estimating the monthly energy production probability in Poland and Hungary, the knowledge base was queried regarding monthly generation levels in Spain. The calculated probabilities are summarized in

Table 6. Probability of energy generation from a 100 kWp photovoltaic system installed in Spain.

Energy [MWh]	Probability ≤	Probability >
5	0	1
10	0	1
15	0.6666	0.3334

. The results demonstrate that, under Spanish geographical and climatic conditions, a 100 kWp photovoltaic system has a probability of 1 for producing 5 MWh and 10 MWh in a month. Additionally, it has a probability of 0.3334 of achieving a monthly output of 15 MWh.

4.1.4. Comparison of the Performance of Photovoltaic Systems Located in Three European Countries

Figure 8 illustrates a performance comparison of the photovoltaic systems located in three different European countries. Monthly differences in energy produced translate into total annual production. This amounts to 170.9533 MWh for Spain, 124.6385 MWh for Hungary, and 108.3136 MWh for Poland. Monthly energy production in Poland and Hungary strongly depends on the season, whereas in Spain, this dependence is much smaller. The amount of energy produced by the newly created generation capacity translates directly into the amount of yellow hydrogen produced.

In Figure 9, the monthly energy production probability of 5 MWh, 10 MWh, and 15 MWh from photovoltaic systems located in three European countries is demonstrated. A 100 kWp peak photovoltaic system built in Malaga, Spain, is capable of generating 5 MWh and 10 MWh with a probability of 1. This means that regardless of the season, it is always expected to produce more than 10 MWh of energy per month. In Poland and Hungary, the probability of producing monthly energy greater than 5 MWh is definitely higher than 0.7, but is also lower than 1. This means that in several months of the year, especially winter, our solar power plant is not able to produce the assumed amount of energy. The installations in Poland and Hungary can produce 10 MWh of energy with a probability of approximately 0.5. Energy below this threshold will be produced in the winter months, as well as in the early spring months and late autumn months. Only the photovoltaic system located in Spain can achieve an energy production of 15 MWh and only with a probability of just over 0.3.

The production of low-emission hydrogen requires the supply of large amounts of energy obtained from RESs. In approximate calculations, it is assumed that the production of 1 kg of hydrogen requires about 50 kWh of energy. The pressure at the outlet of electrolyzers usually ranges from several to several dozen bar. To compress 1 kg of hydrogen to a pressure of 700 bar, about 5 kWh of energy must be supplied. Figure 10 demonstrates the amount of hydrogen produced from specific amounts of monthly energy produced for different pressures. Taking into account the need to compress hydrogen to 700 bar, it can be stated that about 10% less hydrogen is obtained from the same amount of energy. This is a rather significant difference, which encourages scientists and engineers to develop less energy-intensive hydrogen storage technologies.

A company with 100 ÷ 400 kg of hydrogen per month can use it in a variety of industrial, transport, and energy applications, such as the following:

• Fueling hydrogen vehicle fleets—enough to refuel several passenger cars (e.g., Toyota Mirai) or smaller delivery vehicles.
• Supporting industrial processes—hydrogen is a key raw material in the production of chemicals, e.g., ammonia and methanol.
• Reducing emissions in the steel industry—it can replace coke in iron ore reduction processes.
• Powering fuel cells—it can provide electricity and heat in company facilities or mobile power units.
• Process heat production—burning hydrogen in industrial furnaces can reduce CO₂ emissions.
• Storing renewable energy—surplus energy from RESs can be converted to hydrogen and used during periods of low production.
• Powering forklifts and warehouse equipment—hydrogen can replace batteries in electric forklifts.
• Research and development—laboratories can use hydrogen to test hydrogen technologies and advanced fuel cells.
• Synthetic fuel production—hydrogen can be used to synthesize low-emission fuels.
• Support for start-ups and innovation—companies can test new ways to use hydrogen, such as in drones or maritime transport.

Depending on the company’s business profile, hydrogen can help decarbonize, increase energy efficiency, and innovate.

Some of the hydrogen applications listed above do not require high pressures, and the hydrogen pressure at the electrolyzer outlet, which typically ranges from a few to several dozen bar, is sufficient. Therefore, the industrial process can be directly supplied from the hydrogen production system. Any storage of hydrogen at low pressure can take place in metal hydrides. These hydrogen storage systems, which are still being developed, absorb hydrogen at ambient temperature and release it after slightly heating the system. Other hydrogen applications require compression to a pressure of 350 bar, as is the case for powering buses with hydrogen fuel cells. Hydrogen used to power passenger cars requires compression to a pressure of 700 bar. Due to compression to such high pressures, the amount of hydrogen stored in composite tanks on board such vehicles is sufficient to ensure a range exceeding 500 km. In the case of powering vehicles with hydrogen, it is necessary to store it in compressed form until the vehicle arrives to refuel. Hydrogen under pressure is then stored stationarily, usually in metal tanks. The process of refueling a vehicle with several kilograms of hydrogen usually takes several minutes.

For the data presented in Figure 9 and Figure 10, it is worth discussing the possibility of monthly energy production from a photovoltaic system with a peak power of 100 kWp and using it to produce low-emission hydrogen at a pressure of 700 bar. It has been decided to discuss a monthly energy production of 10 MWh. This amount can be produced by a photovoltaic system located in Spain in all months of the year (probability of 1 in Figure 9). In Polish and Hungarian geographical and climatic conditions, the considered power of 10 MWh per month is possible to obtain only in a few months (probability of 0.5 for Poland and 0.58 for Hungary in Figure 9). This means that a photovoltaic system located in Poland is able to produce 10 MWh per month for 6 months of the year and one located in Hungary can achieve this for 7 months of the year. In the remaining months, companies in Poland and Hungary will have to buy energy shortages from the power grid. If they want to obtain low-emission hydrogen, they will have to buy energy from renewable sources with so-called green certificates. For hydrogen to be considered low-emission, it must meet specific standards for greenhouse gas emissions (mainly CO₂) throughout its production, transport, and use cycle. For example, the European Green Deal (RED III Directive) requires that low-emission hydrogen should generate less than 3.38 kg of CO₂ per 1 kg of hydrogen (i.e., a 70% reduction compared to conventional hydrogen production from natural gas). Low hydrogen emissions are confirmed by various types of international certificates. For example, in order to obtain an RFNBO (Renewable Fuels of Non-Biological Origin) certificate for renewable hydrogen, it is necessary to meet specific sustainability criteria and emission standards. This certification is essential to confirm that the hydrogen produced complies with EU renewable energy directives. The main requirement is that the energy used to produce hydrogen must come from renewable non-biological sources, such as wind, solar, and hydroelectric power plants. The producer must also ensure that hydrogen production does not compete with existing demand for renewable energy. It is, therefore, required that hydrogen production facilities are powered by newly developed renewable energy sources. The production of low-emission hydrogen should be time-synchronized with renewable energy generation, meaning that electrolyzers should operate during periods when renewable energy is available. In addition, the location of hydrogen production should be geographically linked to the renewable energy generation site to minimize energy transmission losses. The producer must also implement monitoring and reporting systems that provide transparency and traceability regarding the energy source and emissions associated with hydrogen production.

5. Discussion

5.1. Discussion on an Integrated Research Approach

Combining measurement data from the Photovoltaic Geographical Information System (PVGIS) with the Metalog distribution offers a number of significant analytical and practical benefits, particularly in the context of planning investments in renewable energy sources and low-emission hydrogen production. PVGIS data provides access to reliable, historical information on energy production from photovoltaic systems in various geographic locations. This tool incorporates satellite and meteorological data, offering detailed forecasts of solar energy production under various climatic conditions. However, average or monthly data alone do not account for the variability and risk associated with energy production, which are crucial to consider when designing hydrogen supply systems.

The Metalog distribution bridges this gap, as it is a statistical distribution with a very flexible structure. Unlike classical distributions such as normal or lognormal, Metalog does not require assumptions about the shape of the data distribution—it can accurately represent asymmetric, multimodal, and long-tailed data. This allows for the realistic modeling of electricity production variability in PV systems, taking into account regional specificities and seasonality. This enables probabilistic analysis, which allows for calculating the probability of achieving a specific energy production level (e.g., 5, 10, or 15 MWh per month) and assessing the risk of energy shortages during months with lower solar radiation.

This approach significantly supports investment, operational, and strategic decision making. Companies can plan energy use, the need for energy storage, and external procurement and consider alternative power sources with more precision. Furthermore, it is possible to adapt electrolyzer operation to actual energy conditions, which is crucial for the efficiency of green hydrogen production. The Metalog distribution can be implemented in popular computing environments such as Python, R, Excel, and specialized software (e.g., GeNIe), making it accessible to smaller companies and institutions.

The integration of PVGIS data and statistics makes Metalog a modern, realistic, and flexible tool for modeling uncertainty in photovoltaic energy production. This approach not only increases the quality of analyses, but, above all, supports effective planning of the development of low-emission hydrogen production technologies, especially in the context of micro-installations and local energy transformation strategies.

Demand-side hydrogen usage profiles play a critical role in designing renewable-based hydrogen production systems and optimizing their economic performance. Daily and monthly consumption patterns differ significantly between application sectors: mobility-focused deployments, such as hydrogen refueling stations for buses or passenger vehicles, require a steady, predictable daily supply to maintain operational continuity, whereas industrial processes (e.g., ammonia synthesis, methanol production, and metallurgy) often follow batch or seasonal cycles, allowing for greater flexibility in hydrogen delivery. Aligning production variability with demand is essential to reducing storage requirements and mitigating reliance on external electricity procurement. For instance, high daily demand with a limited tolerance for supply interruptions necessitates larger hydrogen buffer storage or hybrid PV–wind generation to smooth seasonal fluctuations, while monthly or seasonal demand enables the cost-effective utilization of electrolyzer capacity during periods of surplus PV output. The probabilistic PVGIS–Metalog–LCOH framework introduced in this study can be readily extended to incorporate these demand-side profiles, enabling system-level optimization of electrolyzer scheduling, storage sizing, and grid interaction strategies. By explicitly linking production dynamics to end-use requirements, future modeling efforts will provide a more comprehensive evaluation of investment trade-offs and resilience strategies for decentralized hydrogen systems.

5.2. Levelized Cost of Hydrogen Calculations

Combining research data with typical investment and operating cost estimates facilitates the calculation of the approximate cost of hydrogen production (LCOH) for Poland, Hungary, and Spain. Economic data were estimated based on the literature [84,85]. The following assumptions were made for the LCOH calculation:

• PV system capacity: 100 kWp
• Annual energy production (from the article):

  -

  Poland: 108.3 MWh

  -

  Hungary: 124.6 MWh

  -

  Spain: 170.95 MWh

• Energy demand: 50 kWh per 1 kg H₂
• PV system cost (CAPEX): EUR 900/kWp = EUR 90,000 [86]
• Electrolyzer cost (CAPEX): EUR 1000/kW = EUR 100,000 [87]
• Operating cost (OPEX): 3% CAPEX = EUR 5700/year [88]
• System lifetime: 20 years
• Discount rate: 5%

The step-by-step calculation algorithm is presented as follows:

• Annual hydrogen production is calculated from Equation (1), as follows:

$$\mathrm{k}\mathrm{g}{\mathrm{H}}_2={\displaystyle \frac{\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \left[\mathrm{k}\mathrm{W}\mathrm{h}\right]}{50 \left[\mathrm{k}\mathrm{W}\mathrm{h}\right]}}$$

(1)

For each country, we obtain the following annual hydrogen production values:

• Poland: 108,313 kWh → 2166 kg H₂
• Hungary: 124,638 kWh → 2493 kg H₂
• Spain: 170,953 kWh → 3419 kg H₂

2.

LCOH is calculated from Equation (2) [85], as follows:

$$\mathrm{L}\mathrm{C}\mathrm{O}\mathrm{H}={\displaystyle \frac{\mathrm{C}\mathrm{A}\mathrm{P}\mathrm{E}\mathrm{X}·\mathrm{C}\mathrm{R}\mathrm{F}+{\mathrm{O}\mathrm{P}\mathrm{E}\mathrm{X}}_{\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}}}{\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{h}\mathrm{y}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{g}\mathrm{e}\mathrm{n} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \left[\mathrm{k}\mathrm{g}\right]}}$$

(2)

where CRF (Capital Recovery Factor) is calculated from Equation (3), as follows:

$$\mathrm{C}\mathrm{R}\mathrm{F}={\displaystyle \frac{{\mathrm{r}(1+\mathrm{r})}^{\mathrm{n}}}{{(1+\mathrm{r})}^{\mathrm{n}}-1}}$$

(3)

For the assumed values r = 0.05 and n = 20, CRF ≈ 0.08024.

3.

Total costs are as follows:

• Total CAPEX: EUR 90,000 (PV) + EUR 100,000 (electrolyzer) = EUR 190,000
• Annual OPEX: EUR 5700
• Annual CAPEX: EUR 190,000 × 0.08024 ≈ EUR 15,246

4.

The results of the LCOH calculations in three European countries are presented in

Table 7. LCOH calculation results in three European countries.

Country	Annual H2 Production [kg]	Annual Costs [EUR]	LCOH [EUR/kg H2]
Poland	2166	15,246 + 5700 = EUR 20,946	9.67
Hungary	2493	EUR 20,946	8.40
Spain	3419	EUR 20,946	6.13

.

We reach the following conclusions from the LCOH calculations:

• Spain has the lowest LCOH (approximately EUR 6.13/kg) due to having the highest PV energy production and lowest seasonal variations.
• In Poland and Hungary, the cost of hydrogen is higher (EUR 8.4–9.7/kg), primarily due to lower energy production and seasonality.
• The results are consistent with general trends in the literature—green hydrogen production is cheaper in countries with high solar radiation.

The simple LCOH calculation model presented here can be expanded to take into account the degradation of electrolyzer efficiency and the need to replace stacks every few years. The authors performed alternative calculations within this range, taking into account the following: lifetime n = 20 years; discount rate r = 5%; CAPEX (PV + Electrolyzer) = EUR 190,000; fixed OPEX = 3% CAPEX = EUR 5700/year; initial specific energy 50 kWh/kg; degradation 0.8%/year (increase in kWh/kg); reinvestment 40% of system CAPEX (=EUR 76,000) in year 6. Hydrogen output was derived from annual PV energy divided by specific energy each year; LCOH was computed as NPV(costs)/NPV(H₂). The calculation results are presented in

Table 8. Alternative LCOH calculation results in three European countries.

Country	LCOH Base (EUR/kg)	LCOH Alt (EUR/kg)	Δ LCOH (EUR/kg)	Increase vs. Base (%)	NPV Costs Base (EUR)	NPV Costs Alt (EUR)	NPV H2 Base (kg)	NPV H2 Alt (kg)
Spain	6.13	7.93	1.81	29.5	261,035	317,747	42,609	40,049
Hungary	8.40	10.88	2.48	29.5	261,035	317,747	31,065	29,199
Poland	9.67	12.52	2.85	29.5	261,035	317,747	26,997	25,374

.

Under the adopted assumptions (electrolyzer efficiency degradation of 0.8%/year + 40% system CAPEX for stack replacement in year 6), LCOH increases relative to baseline by approximately 29.5%, as follows: Poland from 9.67 to 12.52 EUR/kg, Hungary from 8.40 to 10.88 EUR/kg, and Spain from 6.13 to 7.93 EUR/kg. The relative increase is similar across all locations, but the absolute cost level remains the lowest in Spain and the highest in Poland, confirming the dominant impact of solar resources on LCOH. In practice, economic models must account for the degradation path and stack replacement CAPEX, since ignoring these effects systematically underestimates LCOH by ~30% and may lead to overestimation of the profitability of small-scale installations.

The combined use of PVGIS tools, Metalog distributions, and the LCOH index enables a comprehensive assessment of the potential for hydrogen production from PV, taking into account both local solar radiation conditions and the variability and risk of energy production. This approach allows for realistic hydrogen cost forecasting and informed investment decisions, particularly for SMEs planning an energy transition [89,90].

5.3. Hybrid PV–Wind Solutions for Year-Round Hydrogen Continuity

A practical pathway to reduce the seasonal and diurnal production gaps observed in PV-only systems is to hybridize solar with wind resources. In many European locations, PV and wind profiles are partially complementary, i.e., PV peaks occur in daytime/summer, while wind often contributes more during evenings and winter, thereby smoothing the net renewable profile and improving electrolyzer utilization factors across the year [91]. This complementarity directly addresses the continuity constraints highlighted by our probabilistic PV analysis and can lower both curtailment risk and the minimum hydrogen buffer required to maintain steady output.

Recent studies on hybrid renewable energy systems (HRESs) underscore sizing and operational strategies that co-optimize the mix of generation, storage, and conversion assets for hydrogen pathways. For instance, system-level sizing frameworks that couple PV, wind, batteries, and electrolyzers show that modest wind shares can substantially increase the annual full-load hours on the electrolyzer and reduce reliance on grid imports [43,46]. From a hydrogen-centric viewpoint, integrating wind with PV consistently improves production continuity and can reduce LCOH sensitivity to intra-annual variability [72].

Hybridization also reshapes storage needs. Short-term batteries mitigate sub-hourly ramps and help meet electrolyzer turndown constraints, whereas hydrogen tanks handle multi-day or seasonal imbalances. Dispatch policies that co-optimize battery cycling with electrolyzer loading (respecting stack efficiency curves and minimum load limits) reduce start–stop events and degradation, which is non-trivial for PEM stacks [5].

In parallel, inter-annual PV variability, documented even in high-insolation regions, can be buffered by wind contributions that are less correlated with solar irradiance, further stabilizing yearly hydrogen yield [44].

From a regulatory standpoint, the EU’s RFNBO framework emphasizes the temporal correlation between RES generation and electrolyzer consumption, as well as geographical proximity. A co-located PV–wind hybrid facilitates on-site time-matching (“additionality” and hour-level correlation) and can simplify compliance relative to purchasing certificates ex-post (cf. RFNBO/RED III guidance summarized in our manuscript).

Design implications for PV–Wind–H₂ systems emerging from the literature and our context include the following:

(1)

Mix and sizing: Determine a PV–wind ratio that elevates electrolyzer full-load hours while limiting curtailment; sensitivity runs over several wind penetrations (e.g., 20–50% of annual energy) are informative [43,46].

(2)

Storage layering: Combine battery (intra-day) and H₂ buffer (inter-day/seasonal) to respect electrolyzer dynamics and reduce CAPEX-intensive overbuild [5].

(3)

Operational policy: Adopt dispatch rules that prioritize renewable self-consumption for H₂, use brief battery support to keep the stack within efficient operating windows, and curtail only when both storage layers saturate [72].

(4)

Risk and uncertainty: Evaluate inter-annual envelopes for both PV and wind; hybridization narrows downside risk in weak solar months, which can be reflected in probabilistic LCOH bands [43,44].

Overall, a PV–wind hybrid system is a credible extension of our framework: it leverages the same PVGIS-driven, Metalog-based uncertainty modeling while adding a second, complementary stochastic driver. In future research, authors will extend our probabilistic pipeline to include wind resource distributions and joint-resource scenarios, quantify the resulting increase in electrolyzer utilization, and present LCOH sensitivity surfaces versus PV–wind share, storage capacity, and discount rate, thereby generalizing the present PV-only assessment to a broader class of mixed-RES strategies.

5.4. Energy Storage System Solutions for Year-Round Hydrogen Continuity

An essential aspect of designing renewable-based hydrogen production systems is the strategic integration of energy storage solutions to mitigate the inherent variability of solar generation. While photovoltaic-only systems offer low operational costs and scalability, their intermittency often necessitates a multi-layered storage strategy to ensure continuous electrolyzer operation and stable hydrogen output. Short-term storage, typically in the form of lithium-ion batteries or other fast-response technologies, is effective for managing intra-day fluctuations, reducing the frequent start–stop cycles of the electrolyzer, and improving stack lifetime. For medium- and long-term balancing, hydrogen buffer tanks provide a cost-efficient means of seasonal storage, enabling energy decoupling over days or weeks. Recent studies highlight that combining batteries and hydrogen tanks optimizes system economics: batteries minimize curtailment and ramping penalties, while hydrogen storage addresses low-generation periods without extensive overbuilding of renewable assets [92]. Furthermore, innovative concepts such as metal hydride storage, underground hydrogen caverns, and modular compression systems can further reduce the LCOH by enhancing energy security and reducing grid dependence [93]. Incorporating storage dimensioning and operation into probabilistic modeling frameworks (such as the PVGIS–Metalog–LCOH approach presented here) can provide decision makers with a clearer picture of investment trade-offs, improve electrolyzer utilization rates, and support compliance with regulatory requirements like the EU RFNBO temporal correlation criteria.

5.5. Scalability: Impact of Plant Size and Economies of Scale on LCOH

In this article, the authors only consider the case of a photovoltaic system with a peak power of 100 kWp [94,95]. The following reasonable question arises: How does the LCOH change depending on the scale effect at system capacities reaching several MW?

Assumptions: We scale the PV + electrolyzer system proportionally from 100 kWp to 1 MWp (×10) and 5 MWp (×50). Baseline parameters: n = 20 years, r = 5%, fixed OPEX = 3% of CAPEX/year, 50 kWh/kg H₂.

We consider the following three unit-cost schedules:

• S0 (no scale effect): PV EUR 900/kWp, EL EUR 1000/kW (as in the base case).
• S1 (moderate scale effect, ~1 MW): PV EUR 750/kWp, EL EUR 800/kW.
• S2 (strong scale effect, ~5 MW): PV EUR 600/kWp, EL EUR 500/kW.

Results (LCOH = NPV(costs)/NPV(H₂)):

• Scaling without scale effects (S0): LCOH does not change versus 100 kWp (costs and output rise linearly): Poland EUR 9.67/kg, Hungary EUR 8.40/kg, Spain EUR 6.13/kg.
• 1 MWp, moderate scale effect (S1): LCOH decreases by ~18.4% to EUR 7.89/kg (PL), EUR 6.85/kg (HU), EUR 5.00/kg (ES).
• 1 MWp, stronger effect (S2): decrease of ~34.2% to EUR 6.36/kg (PL), EUR 5.53/kg (HU), EUR 4.03/kg (ES).
• MWp, moderate effect (S1): decrease of ~28.9% to EUR 6.87/kg (PL), EUR 5.97/kg (HU), EUR 4.35/kg (ES).
• MWp, strong effect (S2): decrease of ~42.1% to EUR 5.60/kg (PL), EUR 4.86/kg (HU), EUR 3.55/kg (ES).

Commentary:

(1)

Pure scaling without lower unit costs does not improve LCOH; gains stem from economies of scale (lower EUR/kWp and EUR/kW).

(2)

Relative reductions are similar across locations, yet Spain remains cheapest as a result of having the highest PV yield.

(3)

When we include the previously shown electrolyzer degradation (0.8%/yr) and replacement CAPEX (40% of total system CAPEX in year 6), every scenario increases by approximately 29.5%; for example, Spain 5 MWp, S2: EUR 3.55 → EUR 4.59/kg. In practice, further LCOH reductions require parallel optimization of the supply profile (PV–wind hybrid) and layered storage (battery + H₂ buffer) to raise electrolyzer utilization and limit losses/cycling.

Scaling photovoltaic systems and electrolyzers from 100 kW to 5 MW significantly reduces the cost of hydrogen production due to economies of scale, which reduce the unit capital expenditure (CAPEX) per kWp of PV power and kW of electrolyzer power. This paper assumes that the cost for small PV systems is approximately EUR 900/kWp and the cost for an electrolyzer is EUR 1000/kW. At 5 MW, the costs drop to approximately EUR 600/kWp and EUR 500/kW, respectively, which translates into a LCOH reduction of up to 40%. These savings result from lower purchase costs for modules, inverters, and process equipment, more efficient logistics, and greater automation in the assembly and operation of large installations [96]. Higher capacities also mean higher electrolyzer utilization, which translates into greater hydrogen production through the spread of maintenance and stack replacement costs [97]. The results prove that regardless of the solar location, the scale of investment is one of the key factors in reducing LCOH and increasing the profitability of green hydrogen.

5.6. Sensitivity Analysis and Uncertainty Bounds

We evaluated the robustness of LCOH to the following three key drivers: CAPEX (±20%), electrolyzer specific energy (±10% around 50 kWh/kg, a proxy for efficiency), and discount rate (3%, 5%, and 7%) [98]. For each country, we computed LCOH as NPV(costs)/NPV(H₂) over 20 years with a fixed OPEX equal to 3% of CAPEX per year [99,100]. Tornado plots (r = 5%) show that LCOH is most sensitive to changes in specific energy and CAPEX, followed by the discount rate; the ordering is consistent across locations, while absolute levels reflect the different PV yields (Spain < Hungary < Poland). Tornado plots are shown in Figure 11, Figure 12 and Figure 13, on the left side. The heat maps illustrate the joint effect of CAPEX and specific energy: moving from 55 to 45 kWh/kg and from 1.2× to 0.8× CAPEX reduces LCOH by several EUR/kg, with the largest absolute benefit in lower-yield locations. Heat maps are shown in Figure 8 and Figure 9, on the right side. Across the scenario envelope, the uncertainty bounds at r = 5% span approximately (Poland: ~7–12.7 EUR/kg; Hungary: ~6.2–11.1 EUR/kg; Spain: ~4.4–8.1 EUR/kg), with analogous ranges at r = 3% and 7% (see Summary

Table 9. LCOH uncertainty bounds by country and discount rate (CAPEX ±20%, specific energy ±10%).

Country	Discount Rate	Base LCOH (EUR/kg)	Min LCOH (EUR/kg)	Median LCOH (EUR/kg)	Max LCOH (EUR/kg)	Range (EUR/kg)
Poland	3%	8.53	6.14	8.53	11.26	5.12
Poland	5%	9.67	6.96	9.67	12.76	5.8
Poland	7%	10.91	7.86	10.91	14.4	6.55
Hungary	3%	7.41	5.34	7.41	9.78	4.45
Hungary	5%	8.4	6.05	8.4	11.09	5.04
Hungary	7%	9.48	6.83	9.48	12.52	5.69
Spain	3%	5.4	3.89	5.4	7.13	3.24
Spain	5%	6.13	4.41	6.13	8.09	3.68
Spain	7%	6.91	4.98	6.91	9.12	4.15

Note: If electrolyzer degradation and stack replacement (e.g., +0.8%/year in kWh/kg and 40% system CAPEX in year 6) are included, LCOH levels shift upward by approximately 29–30% across scenarios, while relative sensitivities and qualitative conclusions remain unchanged.

). These results provide transparent ranges for decision makers and clarify where cost reduction efforts (efficiency improvements, capital cost reductions, and financing) most effectively lower hydrogen costs.

The authors added a new sensitivity analysis with the following:

• Tornado plots (one per country, at r = 5%) showing which input drives LCOH the most (CAPEX, specific energy, discount rate).
• Heat maps (one per country, at r = 5%) over a 3 × 3 grid of CAPEX multipliers × specific energy (45/50/55 kWh/kg).
• A summary table of uncertainty bounds (min/median/max LCOH) for each country at r = 3%, 5%, 7% under CAPEX ±20% and specific energy (efficiency) ±10%—see the interactive table titled “LCOH sensitivity summary (bounds by CAPEX ±20%, specific energy ±10%)”.

The sensitivity analysis in this paper demonstrates that the cost of hydrogen production (LCOH) is most sensitive to changes in electrolyzer efficiency, expressed as specific energy consumption (kWh/kg H₂), followed by the CAPEX level, while the discount rate has a relatively smaller impact [101]. Tornado plots clearly indicate that a shift in electrolyzer efficiency of ±10% can change LCOH by several euros per kilogram, making this parameter crucial for technology optimization. In turn, changes of ±20% in CAPEX cause significant differences in LCOH, especially in countries with lower PV productivity, such as Poland. Heat maps reveal the interaction between CAPEX and efficiency—the lowest costs are achieved with a simultaneous decrease in capital expenditures and improvement in efficiency, while negative changes in both parameters drastically increase LCOH. It is also evident that in Spain, due to high PV production, the absolute LCOH level remains lower, even under unfavorable scenarios, while in Poland and Hungary, the variability of these parameters has a stronger impact on the results. The LCOH uncertainty range determined in the analysis (Poland ~7–12.7 EUR/kg; Hungary ~6.2–11.1 EUR/kg; Spain ~4.4–8.1 EUR/kg) demonstrates the significant economic risk associated with location and technical parameters. The results confirm that the most effective way to reduce hydrogen costs is to simultaneously reduce CAPEX and increase electrolyzer efficiency, as clearly illustrated in the tornado and heat map graphs.

6. Conclusions

The online tool developed by the Joint Research Centre (JRC) of the European Commission is effective in determining the monthly energy production of photovoltaic systems in any European location. The authors adopted this tool to compare the performance of systems in three different European countries. An important feature of this tool is the ability to download the calculation results saved in CSV format. This facilitates their further use and processing.

The article presents comparative analyses and probabilistic calculations related to electricity production by 100 kWp photovoltaic systems located in the following three European countries: Poland, Hungary, and Spain. The Metalog probability distribution family was employed to calculate the probability of producing specific monthly levels of electricity for the production of low-emission hydrogen.

The study shows that in the three European countries, a photovoltaic system with a peak power of 100 kW is able to produce very different amounts of energy per year. In Polish geographical and climatic conditions, an annual production of 108.3136 MWh can be expected. In Hungary, this amount is much higher and amounts to 124.6385 MWh, 15% higher than that in Poland. The most energy, 170.9533 MWh, will be produced by photovoltaic systems in Malaga, Spain. This is almost 58% more than in Poland.

In low-emission hydrogen production systems, the continuity of its production in individual months of the year is important. The approach applied by the authors allows for calculating the probability of production of specific monthly levels of electricity, which correspond to the amounts of hydrogen produced. A 100 kWp peak photovoltaic system built in Malaga, Spain, is capable of generating 5 MWh and 10 MWh with a probability of 1. This means that regardless of the season, we can always expect to produce more than 10 MWh of energy per month. In Poland and Hungary, the probability of producing monthly energy greater than 5 MWh is definitely higher than 0.7, but is also lower than 1. This means that in several months of the year, our solar power plant is not able to produce the assumed amount of energy. This applies especially to the winter months. Installations in Poland and Hungary can produce energy of 10 MWh with a probability of approximately 0.5. Energy below this threshold will be produced in the winter months, as well as in the early spring months and late autumn months. Only a photovoltaic system located in Spain can achieve an energy production of 15 MWh, and only with a probability of just over 0.3.

Spain achieves the lowest cost of hydrogen production (approximately EUR 6.13/kg) due to having the highest amount of electricity produced by PV installations and lower seasonal variations. In Poland and Hungary, the cost is higher (EUR 8.4–9.7/kg) due to lower energy production and seasonality. These results are consistent with the literature, which indicates that green hydrogen production is cheaper in countries with high solar radiation.

Under the adopted assumptions (electrolyzer efficiency degradation of 0.8%/year + 40% system CAPEX for stack replacement in year 6), LCOH increases relative to baseline by approximately 29.5%, as follows: Poland from 9.67 to 12.52 EUR/kg, Hungary from 8.40 to 10.88 EUR/kg, and Spain from 6.13 to 7.93 EUR/kg. The relative increase is similar across all locations, but the absolute cost level remains the lowest in Spain and the highest in Poland, confirming the dominant impact of solar resources on LCOH. In practice, economic models must account for the degradation path and stack replacement CAPEX—ignoring these effects systematically underestimates LCOH by ~30% and may lead to overestimation of the profitability of small-scale installations.

The sensitivity analysis presented in this article shows that changes in capital expenditure (CAPEX) and electrolyzer efficiency have the greatest impact on the cost of hydrogen production (LCOH), while the discount rate plays a lesser role. Changing these parameters within the studied range (CAPEX ±20%, energy consumption ±10%) is observed to result in LCOH fluctuations of several euros per kilogram of hydrogen, with the largest differences occurring in locations with lower solar radiation. The results provide clear uncertainty ranges and indicate that actions that reduce CAPEX and increase technology efficiency are the most effective in reducing the cost of green hydrogen.

The presented analyses and probabilistic calculations can be particularly useful for micro and small companies in the conceptual planning of climate and energy transformations. The obtained results can be used by renewable energy developers in planning investments in new energy production capacities for the production of low-emission hydrogen. The obtained quantitative results related to energy production from photovoltaic systems in three different European countries can be a starting point for making decisions on investment location. Investors should take into account the geographical requirements for the production of low-emission hydrogen in order to minimize losses related to energy transmission and the costs of hydrogen transport to potential distribution points.