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Article

Probabilistic Analysis of Green Hydrogen Production from a Mix of Solar and Wind Energy

by
Agnieszka Dudziak
1,*,
Arkadiusz Małek
2,*,
Andrzej Marciniak
2,
Jacek Caban
3 and
Jarosław Seńko
4
1
Department of Power Engineering and Transportation, Faculty of Production Engineering, University of Life Sciences in Lublin, 20-612 Lublin, Poland
2
Department of Transportation and Informatics, WSEI University, 20-209 Lublin, Poland
3
Department of Automation, Faculty of Mechanical Engineering, Lublin University of Technology, 20-618 Lublin, Poland
4
Institute of Vehicles and Construction Engineering, Faculty of Automotive and Construction Machinery Engineering, Warsaw University of Technology, 02-524 Warszawa, Poland
*
Authors to whom correspondence should be addressed.
Energies 2024, 17(17), 4387; https://doi.org/10.3390/en17174387
Submission received: 22 July 2024 / Revised: 26 August 2024 / Accepted: 30 August 2024 / Published: 2 September 2024
(This article belongs to the Special Issue Advanced Forecasting Methods for Sustainable Power Grid)
Browse Figures
Versions Notes

Abstract

This article describes an example of using the measurement data from photovoltaic systems and wind turbines to perform practical probabilistic calculations around green hydrogen generation. First, the power generated in one month by a ground-mounted photovoltaic system with a peak power of 3 MWp is described. Using the Metalog family of probability distributions, the probability of generating selected power levels corresponding to the amount of green hydrogen produced is calculated. Identical calculations are performed for the simulation data, allowing us to determine the power produced by a wind turbine with a maximum power of 3.45 MW. After interpolating both time series of the power generated by the renewable energy sources to a common sampling time, they are summed. For the sum of the power produced by the photovoltaic system and the wind turbine, the probability of generating selected power levels corresponding to the amount of green hydrogen produced is again calculated. The presented calculations allow us to determine, with probability distribution accuracy, the amount of hydrogen generated from the energy sources constituting a mix of photovoltaics and wind. The green hydrogen production model includes the hardware and the geographic context. It can be used to determine the preliminary assumptions related to the production of large amounts of green hydrogen in selected locations. The calculations presented in this article are a practical example of Business Intelligence.

1. Introduction

With Poland being a European Union member state, the Polish industry is currently undergoing climate and energy transitions. The requirements of the European Green Deal force pro-ecological changes in many branches of industry and life. Due to the legislative changes mentioned above, but also due to evident economic benefits, Polish people are very eager to use renewable energy sources (RESs). The number of home and industrial photovoltaic installations has grown significantly in recent years. In 2024, the energy produced from distributed photovoltaic (PV) systems already constitutes a significant part of the energy produced. The total peak power generated by the photovoltaic systems installed in Poland at the end of April 2024 was approximately 17.9 GW. Photovoltaics constitute 60.27% of the installed renewable energy capacity. The second place is taken by wind farms, generating a power of 9.5 GW, which constitutes 32.05% of the installed renewable energy capacity [1]. The year 2023 brought significant changes in the Polish energy generation mix. For the first time in history, the share of coal usage in electricity production dropped to 60.5%. It was mainly renewable sources that replaced coal-fired energy production, accounting for a record 27% of the total power generation [2]. Polish people consider investing in electricity production capacity from RESs as a way of becoming independent from the ever-increasing prices of electricity supplied by domestic producers and sellers of energy, especially that generated from fossil fuels. Being a prosumer of electricity is currently a trend in Poland [3]. This trend applies especially to individual households: having an installation generating energy from renewable energy sources is becoming a necessity, especially for small- and medium-sized Polish enterprises (SMEs). Without the cheap energy from RESs, they are unable to compete with the prices available from other entities/institutions that have their own RESs [4]. In the case of SMEs, the profitability of investing in photovoltaic systems depends especially on auto-consumption. Companies that need large amounts of electricity during the day, especially in the summer, are eager to invest in PV systems. This energy demand profile fits perfectly into the power generation characteristics of photovoltaic systems since they produce energy only when the sun is shining. The amounts of energy produced in the Polish climatic and geographical conditions are strongly dependent on the seasons. Companies that need high amounts of power all the time or only use it at night are in a more difficult situation. Such companies should diversify their sources of power generation. It is worth considering wind farms, which do not depend on day/night cycles for energy production [5].
However, the climate and energy transformation of entire countries cannot be based on stationary energy storage facilities [6]. Scientists have recognized hydrogen as a medium that can significantly support the climate and energy transformation at the level of entire countries and individual companies, regardless of their size [7,8]. This is due to many physico-chemical properties of hydrogen. The first such property is the widespread availability of hydrogen. Clean hydrogen can be obtained from publicly available water using various technologies. However, each hydrogen production technology requires a large amount of electricity and heat [9]. Another important feature of hydrogen is its ecology. Using hydrogen fuel cell technology, electricity and heat can be generated from hydrogen without any major problems, for both stationary and mobile applications. At the current stage of the world’s climate and energy transformation, storing and transporting hydrogen over longer distances is still rather challenging [10,11].
Distinct actions within this climate and energy transition must cover the entire technology and value chain for the generation, transport, and use of hydrogen in various industries [12]. They require huge investments both in new capacities for generating energy from RESs and in the technologies for the production and use of hydrogen [13]. It is not possible for only entrepreneurs to bear the costs of such a transformation. This action must be based on effective public–private investments. Poland as a country is aware of this. The Polish Hydrogen Strategy until 2030 with a perspective until 2040 (PHS) is a strategic document that defines the main goals of the development of the hydrogen economy in Poland and the directions of actions necessary to achieve them. The PHS is part of global, European, and national activities aimed at building a low-emission economy. The vision and primary goal of the PSW is to create a Polish branch of the hydrogen economy and its development to achieve climate neutrality and maintain the competitiveness of the Polish economy [14]. A very important document of strategic importance is the “Forecast of demand for renewable hydrogen in Poland until 2030” [15]. This report, prepared by a team of scientists led by Dr. Grzegorz Tchorek, professor at the Institute of Energy, concerns the industrial sector (chemical industry, refinery, metallurgy, heating, and power engineering) and transport (by sea, air, and land).
The authors’ visits to the hydrogen fairs in Bremen (Hydrogen Technology Conference and Expo 2023) and Paris (Hyvolution 2024) and the renewable energy technology fair in Munich (Intersolar Europe 2024) confirm the presence, on the European and global markets, of technologies for hydrogen generation using energy from RESs, alongside its storage [16], transport, and usage in many industrial sectors [17]. These are mature technologies that one can purchase and use in a private company. According to the authors, entrepreneurs expect support from scientists in defining exemplary concepts for the decarbonization of specific industries [18]. Companies producing artificial fertilizers and industrial chemicals or using hydrogen as a fuel in transport applications will require differing scales of hydrogen production. A very important area of support for entrepreneurs planning on making such an investment covers the estimation of the size and location of the RES production system [19]. Case studies showing good practices have already been implemented, with highly desirable successes. The authors, having scientific and market experience in the area of generating energy from RESs and the use of various hydrogen technologies, in this and subsequent articles aim to support many players in current efforts towards effective climate and energy transition using hydrogen.
The green hydrogen needs for companies in the Lublin region are enormous. The Grupa Azoty Zakłady Azotowe Puławy factory is located in the Lubelski Voivodeship. It is common knowledge that this company, which produces artificial fertilizers and industrial chemicals, has produced and used approximately 230,000 tons of gray hydrogen in recent years. This type of hydrogen was and still is produced using steam-reforming methods from methane [20]. In order to maintain its current product portfolio, the company will have to replace gray hydrogen with its green equivalent in the near future [21]. This is a consequence of the RED III Directive (Renewable Energy Directive III), which is the European Parliament’s response to the need to increase the use of energy from RESs to achieve the aims of the Green Deal and REPower EU. It was adopted in October 2023, giving member states 18 months to transpose the new provisions into national law. The amendment to the Directive posits that EU Member States will have to obtain 45% of energy from renewable energy sources by 2030. Poland has been forced to implement measures to achieve these goals in heating, energy, industry, and transport.
The following question often arises: Where should one produce hydrogen [22]? Scientists compare the efficiency and costs of green hydrogen generation from wind farms located at sea and on land [23,24]. The authors propose the Lubelski Voivodeship as the best place in Poland to invest in renewable energy and hydrogen technologies. The Lublin region has enormous development opportunities in the field of RESs and possibilities of cooperation in the energy field with Ukraine. As previously indicated, the Lubelski Voivodeship has some of the best wind conditions in Poland. This is because the total, but currently still theoretical, potential areas suitable for the construction of wind farms cover 2000 square kilometers, i.e., 8% of the voivodeship area. Currently, there are approximately 100 windmills in the Lublin region, mostly concentrated within nine wind farms [25], while even more are under construction. In the coming years, 10 to 20 farms with up to 200 windmills could be built. The benefit for the municipalities is also important. The construction of a wind farm creates new job opportunities and additional budget revenues [26].

2. Materials and Methods

The authors decided to first calculate the production of energy from RESs and the amount of green hydrogen produced over a period of one month [27,28]. Such calculations make sense due to the monthly payments of companies to the seller and supplier of electricity. The strategic model is also intended to support concept-level calculations carried out by renewable energy developers and production companies involved in green hydrogen generation [29,30]. At a time when companies in Europe need to implement climate and energy transformation, this is of great importance [31,32]. The flow diagram of measurement data acquisition and processing in the article is presented in Figure 1.
Calculations of this type supplemented with economic data can be used to calculate the price of green hydrogen for the manufacturer to apply for funding for green hydrogen generation from the European Hydrogen Bank [33].
The authors of this article already have extensive experience in using the Metalog probability distribution family. It has been used in many studies conducted in the field of energy generation from RESs and its use in transport [34]. Among other things, these studies demonstrated its usefulness in preparing a strategic model for yellow hydrogen generation [35]. Recently, the authors used this tool to determine the technical condition of traction batteries from hybrid vehicles [36]. The authors also use innovative tools and a modern approach to designing energy generation, storage, and distribution systems [37]. Algorithms employing artificial intelligence are increasingly used for this purpose [38,39].
The authors present, in this article, the use of the Genie Academic 4.1 software tool based on the Metalog probability distribution family. They show how the tool creates PDF and CDF, which are models based on probability theory. They constitute a knowledge base, unlike commonly known and used databases. The theory itself and the programming tool are very well described in the literature, including, among others, their creator Thomas Keelin. In the current article, the authors especially focused on the practical way of obtaining knowledge from this knowledge base.

3. Results

In this section, the authors will first characterize and analyze the data describing energy production by photovoltaic systems. Then, they will perform a similar analysis for the data describing the operation of wind turbines [40]. The final step will be to overlay two time series from PV systems and wind turbines to determine the probability of producing certain levels of electricity in such a combination [41,42].

3.1. Characteristics of Energy Production by Photovoltaic Systems

As previously mentioned in the Introduction, the Lublin region is characterized by good sunlight and, therefore, the largest amounts of energy generated from a photovoltaic system with a specific peak power that can be expected in Poland. The authors have been dealing with the design, construction, and operation of ground-based photovoltaic systems for over 10 years. We are perfectly aware that the performance of PV systems depends on the quality of the selected components and the conditions of their installation. For the purposes of this article, we decided to use data related to the amount of power generated over time by a ground-based photovoltaic system in the form of a carport, with a peak power of 3 kWp. The system was built with 12 monocrystalline panels using glass-glass technology, with an inclination angle of 30° and an azimuth pointing exactly south. The load factor of the photovoltaic system for the previous year (2023) was as follows: 3203 kWh/365/24 h/3 kWp = 0.122 = 12.2%. Due to the use of an advanced inverter, the photovoltaic system transmits the measurement data regarding its operating parameters and performance to the cloud server. The most important data include the value of the generated voltage and current, which allows one to calculate the instantaneous power generated by the photovoltaic system. In the era of Internet of Things devices, it is now standard for the owner of a photovoltaic system to be updated about its performance and technical conditions. Experienced authors in the field of monitoring and managing photovoltaic systems indicate that various manufacturers of photovoltaic inverters provide both the companies installing such systems and their owners with various functions related to the ability to read and report data regarding the system’s operation. The authors were therefore able to obtain data on the operation of photovoltaic systems to check their temporary performance, monitor the accuracy of their operation, and diagnose and repair selected components. Additionally, the authors processed the data available on the cloud server for the energy management purposes of the Lublin Science and Technology Park and the WSEI University in Lublin [43]. The authors’ previous paper clearly confirms that the measurement data from photovoltaic systems can be applied to determine the battery size of an electric vehicle planned for purchase [44]. The approach presented in this article, therefore, involves obtaining and off-line processing measurement data from renewable energy generation systems to determine the amount of green hydrogen generated.
Figure 2 presents the time series of power production for a photovoltaic system with a peak power of 3 MWp in May 2024. This was obtained by scaling the system with a peak power of 3 kWp described in the previous section. Measurement data were recorded every 15 min. The obtained data were multiplied by 1000 and, according to the authors, can be used for simulation research. The time series of generated power clearly shows the periodicity of power generation by the photovoltaic system resulting from day and night cycles. Moreover, the value of the instantaneously generated power is additionally influenced by day-time changes in cloud cover, air temperature, and the speed of the wind passing through the panels. Using only the energy generated by photovoltaic systems during yellow hydrogen production is associated with many limitations, which the authors have referred to in their previous papers.
Figure 3 depicts the histogram of the power produced by the PV system with a peak power of 3 MWp in May 2024, with a normal distribution. It clearly shows that the highest probability density is observed in operations with a power of 0 W. This corresponds to night periods, when the photovoltaic system does not work at all. The remaining levels of useful, generated power fall in the remaining 19 ranges. The probability densities are noticeably close to each other. We can also state with certainty that the probability density distribution does not in any way resemble a normal distribution (the thin line in Figure 3).
The measurement data after scaling were subjected to basic and extended statistical calculations, the results of which are presented in Table 1 and Table 2. It can be seen that the mean value of power generated by the photovoltaic system at peak power is 744.59 kW, with a large standard deviation of 915.335 kW. It is worth noting that the maximum power was 3188 kW and that it exceeded the peak value. This situation happens very rarely in Polish climatic and geographical conditions. This proves the need for the selection of the best components for building a photovoltaic system and a good location for the investment. The academic version of the Genie 4.1 tool [45] was used for the statistical calculations and the modeling of power generation by photovoltaic systems and wind turbines.
Bayes Fusion’s Genie 4.1 tool allowed us to generate a family of Metalog probability distributions for our time series. Figure 4 depicts the cumulative distribution function (CDF) and probability density function (PDF) for the simulation data presented earlier. First, the cumulative distribution function (CDF) was generated (the top chart), along with the characteristic points corresponding to the percentile calculations (yellow markers). The schedule presented in Table 1 and Table 2 has been supplemented with the PDF, i.e., the probability density function (bottom chart). The shape of the PDF clearly indicates where the maximum probability density is located. By comparing the PDF shape for different PV systems, optimizations can be made related to the selection of the best photovoltaic systems for the purposes of green hydrogen production. The power generation model takes into account both the hardware context (the selection of the components and the structure itself) and the geographical context (related to the location).
The model of the Metalog family of probability distributions also has a rather convenient feature [46], which manifests as a knowledge base from which information can be obtained. The Genie 4.1 software, in its academic version, made it possible for us to ask the following question: What is the probability that a system with a peak power of 3 MWp will generate less than or equal to 500 kW in May 2024? The response values are included in Table 2 (bottom rows) and Table 3. The result provided by the knowledge base is 0.5953. Therefore, to obtain the following information, which is more interesting to us—i.e., What is the probability of the system generating a power greater than 500 kW?—a simple subtraction should be performed: 1 − 0.5953 = 0.4047. The authors decided to round the obtained calculation results to four decimal places. Identical calculations were made for the remaining power levels of interest: 1000 kW, 2000 kW, and 3000 kW.
A major disadvantage of Internet of Things devices is their inability to record the acquired measurement data at a desired frequency. Due to the lack of formal and legal requirements in this area, each manufacturer of photovoltaic inverters sends the measurement data to a cloud server over a period of time selected by its engineers. Due to the need to standardize the time series obtained from the photovoltaic system (every 15 min) and the wind turbines (every 10 min—to be described in the next section), it was necessary to interpolate the time series presented in Figure 3 to the least common period of 30 min. A question immediately arose regarding the impact of interpolation on the modeling results. Due to the above concern, identical calculations were performed for the time series after interpolation. The results of these calculations are presented in Figure 5 and Table 4, Table 5 and Table 6.
As a result of this interpolation, the time series of the power generated by the photovoltaic system lost half of its measurement values. By comparing subsequent statistical data before (Table 1) and after interpolation (Table 4), we could see that the minimum and maximum values did not change. The mean and standard deviation changed slightly, by 0.23% and 0.36%, respectively. Our extended quantile analysis for the time series before and after interpolation showed no significant differences.
Such small changes in the basic and extended statistical calculations imply that interpolation should also have a very small impact on the computational model in the form of the cumulative distribution function (CDF) and the probability density function (PDF) presented in Figure 5.
Table 6 presents the results of the knowledge base queries about the probability of generating specific power levels by the photovoltaic system based on the time series after the interpolation procedure.
Table 7 features the results of the probability of obtaining a power greater than the assumed power levels for a 3 MWp PV system before and after interpolation. The relative error between these two values is also calculated.
The relative error in the probability calculations was relatively small for power levels of 500, 1000, and 2000 kW. However, for the power level of 3000 kW, the error was over 100%. It should be noted that this error concerns probability calculations with a very small value, at the level of the fourth decimal place. This results from the fact that, because of interpolation, several measurement points were lost towards peak photovoltaic system production, which took place on 31 May 2024. During this time, the actual power generated by the PV system exceeded the peak power of the system in a short period of time. Taking into account the above circumstances, it can be concluded that the interpolation of the time series of power generated by the photovoltaic system did not have a significant impact on the calculation of the probability of generating specific power levels.

3.2. Characteristics of Energy Production by Wind Turbines

The most reliable method of obtaining the characteristics of energy generation by a wind turbine in a specific location is to erect a measurement tower and perform year-round measurements of wind speed [47,48]. There are also simulation techniques, but they have their accuracy and limitations [49,50,51].
Throughout 2016, the authors carried out the measurements using the measuring tower in the location they were interested in, in the Lublin region. The 140 m high tower was equipped with two wind speed sensors. The measurement data from a period of 10 min of operation were averaged and sent to the cloud server. The resulting wind speeds at the rotor hub height were used together with the power curve of the 3.45 MW Vestas V126 wind turbine to obtain a time series of power produced [52]. Figure 6 shows the time series of power production for a 3.45 MW wind turbine in May 2016. The appropriateness of placing the measurement tower in the selected location was confirmed by the subsequent location of the wind turbine, in the same place.
The probability densities shown in the histogram (Figure 7) have significantly different values in the considered ranges of generated power than the data from the power generated by the 3 MWp PV system presented in Figure 2. Also, the probability density distribution of the power produced by the wind turbine does not show any similarities to the normal distribution (thin line in Figure 7).
In Table 8, one can observe that the average value of the power generated by a 3.45 MW wind turbine is 980.951 kW, with a large standard deviation of 911.637 kW. It is worth noting that the maximum power is 3450 kW. The probability of wind turbine operation in the selected percentiles can be read in Table 9.
Figure 8 shows the cumulative distribution function (CDF) and probability density function (PDF) for the previously presented simulation data of the power produced by the turbine with a maximum power of 3.45 MW. First, the cumulative distribution function (CDF) was generated (top chart) along with the characteristic points corresponding to the percentile calculations (yellow markers). The PDF shape (bottom chart) clearly indicates where the maximum probability density is located. By comparing the PDF shape for different wind turbines, optimizations can be made related to the selection of the best equipment combinations and the best locations for the purposes of green hydrogen production. The model of power generation by a wind turbine takes into account both the hardware context (the selection of the components and the structure itself) and the geographical context (related to its location).
The Genie 4.1 software, in its academic version, made it possible to ask the following question: What is the probability of a system with a maximum power of 3 MW generating less than or equal to 500 kW in May 2016? The response values are included in Table 9 in the bottom rows and complete, in tabular form, in Table 10. The result provided by the knowledge base is 0.3979 Therefore, to obtain information that is more interesting to us—i.e., What is the probability of the system generating a power greater than 500 kW?—a simple subtraction should be performed: 1 − 0.3979 = 0.6021. The authors decided to round the obtained calculation results to four decimal places. Identical calculations were made for the remaining power levels of interest: 1000 kW, 2000 kW, and 3000 kW.
Due to the need to standardize the time series obtained from the photovoltaic system (every 15 min) and wind turbines (every 10 min), it was necessary to interpolate the time series presented in Figure 6 to the least common period of 30 min. Also, in the case of wind turbines, a question arose regarding the impact of interpolation on the modeling results. Due to the above concern, identical calculations were made for the time series after interpolation. The results of these calculations are presented in Figure 9 and Table 11, Table 12 and Table 13.
As a result of interpolation, the time series of the power generated by the wind turbine lost 2/3 of the measurement values. Comparing subsequent statistical data before (Table 8) and after interpolation (Table 11), we could observe that the minimum and maximum values had not changed. The mean and standard deviation changed very little, by 0.23% and 0.59%, respectively. Our extended quantile analysis for the time series before and after interpolation showed no significant differences. Such small changes in the basic and extended statistical calculations led us to assume that interpolation should also have a very small impact on the computational model in the form of the cumulative distribution function (CDF) and probability density function (PDF), which are presented in Figure 9.
Table 13 presents the results of the knowledge base queries about the probability of a wind turbine with a maximum power of 3.45 MW generating specific power levels based on the time series after interpolation.
Table 14 presents the results regarding the probability of obtaining a power greater than the assumed power levels for a wind turbine with a maximum power of 3.45 MW, before and after interpolation. The relative error between these two values is also calculated.
The relative error in the probability calculations is small for all power levels of 500, 1000, 2000, and 3000 MW. Also, in this case, it can be concluded that the interpolation of the time series of the power generated by the wind turbine did not have a significant impact on the calculations of the probability of generating specific power levels.

3.3. Energy Production Characteristics of a Mix of Photovoltaic Systems and Wind Turbines

Scientists and engineers have long concluded that green hydrogen should be produced using hybrid systems of renewable energy sources [53,54,55]. In this context, it is justified to use various techniques and algorithms for predicting electricity production in photovoltaic and wind systems and their combination [56,57,58]. Due to the need to standardize the time series obtained from the photovoltaic system (every 15 min) and the wind turbines (every 10 min), it was necessary to interpolate the time series presented in Figure 3 and Figure 8 to the least common period of 30 min. Then, two time series were added together after interpolation. The time series of power production for the 3 MWp PV system and the wind turbine with a capacity of 3.45 MW are presented in Figure 10.
In Table 15, one can see that the average value of power generated by the 3 MWp PV system and the 3.45 MW wind turbine is 1721.55 kW, with a large standard deviation of 1142.87 kW. It is worth noting that the maximum power obtained with the simultaneous operation of both systems is 6032 kW. The probability of operation of the photovoltaic system and wind turbine in the selected percentiles can be read in Table 16.
Figure 11 shows the cumulative distribution function (CDF) and the probability density function (PDF) for the previously presented simulation data of the power generated by a photovoltaic system with a peak power of 3 MWp and a turbine with a maximum power of 3.45 MW. First, the cumulative distribution function (CDF) is generated (top chart), along with the characteristic points corresponding to the percentile calculations (yellow markers). The PDF shape (bottom chart) clearly indicates where the maximum probability density is located. By comparing the PDF shape for different power combinations of photovoltaic systems and wind turbines, optimizations can be made related to the selection of the best equipment combinations and the best locations for the purposes of generating green hydrogen. The model of power generation by a photovoltaic system and a wind turbine takes into account both the hardware context (the selection of the components and the structure itself) and the geographical context (related to its location). The final model also accounts for the proportion of total energy produced from these two specific sources. In the case of obtaining energy from a photovoltaic–wind mix, the PDF optimum moves to around 1500 kW.
The Genie 4.1 academic software allowed us to ask the following question: What is the probability of generating a power less than or equal to 500 kW by a 3 MWp peak photovoltaic system and a 3.45 MW wind turbine? The response values are included in Table 16 in the bottom rows and in Table 17. The result provided by the knowledge base is 0.1708. Therefore, to obtain the information that is more interesting to us—i.e., what is the probability of the system generating a power greater than 500 kW?—a simple subtraction should be performed: 1 − 0.1708 = 0.8292. The authors decided to round the obtained calculation results to four decimal places. Identical calculations were made for the remaining power levels of interest: 1000 kW, 2000 kW, and 3000 kW.

4. Discussion

The probability of generating specific power levels using the PV system with a peak power of 3 MWp, the wind turbine with a maximum power of 3.45 MW, and by combining these two sources is shown in Figure 12. The graph clearly depicts that higher probability values occur for the wind source with a power of 500 kW and 1000 kW. The photovoltaic source is more likely to achieve a power of 2000 kW during the analyzed month. Only a wind turbine can generate a power of 3000 kW with a probability of less than 4%. The authors would like to emphasize, once again, that the presented probabilistic analysis was performed only for one month of the year—May. The analysis takes into account the local geographical and climatic conditions in which both power generation systems are located—the Lublin region in Poland. Based on the authors’ involvement in the management of many photovoltaic systems of different power levels, it should be emphasized that the month of May, under Polish weather conditions, is one of the months with the highest energy production from photovoltaic systems and one of those with the lowest production from wind systems. Thought-provoking conclusions can be drawn from the probability of generating power from the photovoltaic–wind energy mix. The graph demonstrates that the probability of generating specific amounts of power for both sources is always much higher than the probability for only one source. This leads to a simple conclusion that both sources complement each other extensively. This can be seen by superimposing both of the time series of the generated power. At this point, one can notice that the photovoltaic system generates energy only when the sun is shining, i.e., only during the day. A wind turbine generates power when the wind blows, regardless of the time of day. The large increase in the probability of generating power from the mix compared to the individual sources results from the fact that photovoltaic systems are supported by a wind turbine, especially at night. The authors intend to use the presented computational algorithm in further research for all months of the year. Probabilistic analysis will then be used to determine the cyclicality in energy generation and power production by photovoltaic systems and wind turbines due to the changing seasons.
The probability of generating specific power levels using the photovoltaic system with a peak power of 3 MWp, the wind turbine with a maximum power of 3.45 MW, and by combining these two sources in May can be easily translated into the probability of hydrogen production. Taking into account the simple relationship according to which the production of 1 kg of hydrogen requires an energy of 50 kWh, we can obtain the probability of the hourly production of specific amounts of hydrogen. This is shown in the column charts in Figure 13.
Such a simple translation of the probability of generating specific power levels into hourly hydrogen production can be used to determine the conceptual parameters of a green hydrogen generation plant. From the data presented in Figure 13, it is also possible to approximately determine the power of the electrolyzer, which can be powered with the energy from the photovoltaic–wind energy mix [59,60,61]. According to the authors, the renewable energy sources analyzed in this article can successfully power an electrolyzer with a capacity of 1 MW, provided that small, stationary energy storage is used. However, such calculations will be the subject of subsequent scientific articles by the authors.

5. Conclusions

In this article, the authors presented an algorithm for calculating the probability of generating specific power levels and, thus, the probability of the hourly generation of green hydrogen by RESs. The authors first described the power generated by ground-based photovoltaic systems. A method of scaling the performance of a 3 kWp photovoltaic system to 3 MWp was presented. Then, the method of modeling the power generated by a wind turbine with a maximum power of 3.45 MW was introduced. The Metalog family of probability distributions was applied to perform advanced statistical and probabilistic analyses for individual renewable energy sources separately and for the mix of power produced using both sources. Although this analysis covers only one month of the year, it indicates an effective way of obtaining and processing measurement data from various power generation resources and other measurement sources. The analysis accounts for the local geographical and climatic conditions in which both power generation systems are located, i.e., the Lublin region in Poland. This geographical context is the result of the use of data from this area in the current research. The charts presented in this article demonstrate that the probability of generating specific power levels for both sources is always higher than the probability for only one source. This leads to the conclusion that both sources greatly complement each other. This can be seen by superimposing both of the time series of the generated power. However, the applied analysis using the Metalog family of probability distributions allows it to be described quantitatively, with probability distribution accuracy.
The simple translation of the probability of generating specific power levels into hourly hydrogen production presented in this article can be employed to determine the conceptual parameters of a green hydrogen plant. From the data presented in this article, it is also possible to approximately determine the power of the electrolyzer, which can be powered using the energy from the photovoltaic–wind energy mix. According to the authors, the renewable energy sources analyzed in this article can successfully power an electrolyzer with a capacity of 1 MW, provided that small, stationary energy storage is used. However, such calculations will be the subject of subsequent scientific articles by the authors.
In the future, the authors intend to continue the research they have begun. An area that requires support concerns the optimization of the selection of individual energy sources and the process of generating green hydrogen, especially using electrolytic methods. Interesting areas of research include the reliability aspects of hydrogen production, leading to the construction and practical use of the reliability structure of the entire green hydrogen generation system. Bayesian networks and the Genie software that have already been used by the authors can be used for this purpose. The authors also intend to build a green hydrogen production system powered by energy from a PV carport in the Lublin Science and Technology Park. This real research station will allow for the validation of research performed using simulation tools and the acquisition of real measurement data for processing using artificial intelligence tools.

Author Contributions

Conceptualization, A.M. (Arkadiusz Małek), J.C. and A.D.; methodology, A.M. (Arkadiusz Małek); software, A.M. (Andrzej Marciniak); validation, J.C. and A.D.; formal analysis, A.D. and A.M. (Andrzej Marciniak); investigation, A.M. (Arkadiusz Małek); resources, J.C. and J.S.; data curation, A.M. (Arkadiusz Małek); writing—original draft preparation, A.D., A.M. (Arkadiusz Małek), J.C. and J.S.; writing—review and editing, A.M. (Arkadiusz Małek), J.C., A.D. and A.M. (Andrzej Marciniak); visualization, A.M. (Arkadiusz Małek); supervision, A.D., A.M. (Andrzej Marciniak) and A.M. (Arkadiusz Małek); project administration, A.D.; and funding acquisition, A.D. and J.C. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by an application for the “Szybka Ścieżka 1_2020” competition for cofinancing project no. POIR.01.01.01-000394/20 on the “Development of an innovative power supply module for an electric driven bus using hydrogen and methanol as fuel to charge the vehicle’s battery while in the motion”.

Data Availability Statement

The original contributions presented in this study are included in the article; further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

RESRenewable energy source
PEMProton exchange membrane
AEMAion exchange membrane
AFC Alkaline fuel cell
SOFCSolid oxide fuel cell
SOESolid oxide electrolyzer
MCFCMolten carbonate fuel cell
FCVFuel cell vehicle
PVPhotovoltaic

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Energies 17 04387 g001
Figure 1. Data flow diagram.
Figure 1. Data flow diagram.
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Figure 2. Time series of power generation by a 3 MWp PV system in May 2024.
Figure 2. Time series of power generation by a 3 MWp PV system in May 2024.
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Figure 3. Histogram of power generated by a 3 MWp PV system in May 2024, with a normal distribution (thin line).
Figure 3. Histogram of power generated by a 3 MWp PV system in May 2024, with a normal distribution (thin line).
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Figure 4. Cumulative distribution function (CDF) and probability density function (PDF) for the power produced by a 3 MWp PV system in May 2024.
Figure 4. Cumulative distribution function (CDF) and probability density function (PDF) for the power produced by a 3 MWp PV system in May 2024.
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Figure 5. Cumulative distribution function (CDF) and probability density function (PDF) for the power generated by a 3 MWp photovoltaic system, after interpolation.
Figure 5. Cumulative distribution function (CDF) and probability density function (PDF) for the power generated by a 3 MWp photovoltaic system, after interpolation.
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Figure 6. Time series of power production for a 3.45 MW wind turbine in May 2016.
Figure 6. Time series of power production for a 3.45 MW wind turbine in May 2016.
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Figure 7. Histogram of the power produced by the 3.45 MW wind turbine with a normal distribution.
Figure 7. Histogram of the power produced by the 3.45 MW wind turbine with a normal distribution.
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Figure 8. Cumulative distribution function (CDF) and probability density function (PDF) for a 3.45 MW wind turbine.
Figure 8. Cumulative distribution function (CDF) and probability density function (PDF) for a 3.45 MW wind turbine.
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Figure 9. Cumulative distribution function (CDF) and probability density function (PDF) for a 3.45 MW wind turbine after interpolation.
Figure 9. Cumulative distribution function (CDF) and probability density function (PDF) for a 3.45 MW wind turbine after interpolation.
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Figure 10. Time series of power production for the 3 MWp PV system and the 3.45 MW wind turbine.
Figure 10. Time series of power production for the 3 MWp PV system and the 3.45 MW wind turbine.
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Figure 11. Cumulative distribution function (CDF) and probability density function (PDF) for the 3 MWp PV system and the 3.45 MW wind turbine.
Figure 11. Cumulative distribution function (CDF) and probability density function (PDF) for the 3 MWp PV system and the 3.45 MW wind turbine.
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Figure 12. The probability of generating specific power levels using the 3 MWp PV system, the 3.45 MW wind turbine, and by combining these two sources in the month of May.
Figure 12. The probability of generating specific power levels using the 3 MWp PV system, the 3.45 MW wind turbine, and by combining these two sources in the month of May.
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Figure 13. Probability of generating specific levels of hourly hydrogen production using a system powered by the 3 MWp PV system, the 3.45 MW wind turbine, and by combining these two sources in the month of May.
Figure 13. Probability of generating specific levels of hourly hydrogen production using a system powered by the 3 MWp PV system, the 3.45 MW wind turbine, and by combining these two sources in the month of May.
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Table 1. Basic statistical analysis of the power produced by a 3 MWp PV system in May 2024.
Table 1. Basic statistical analysis of the power produced by a 3 MWp PV system in May 2024.
Power [kW]
Count2975
Minimum0
Maximum3188
Mean744.59
StdDev915.335
Table 2. Extended statistical analysis of the power produced by a 3 MWp PV system in May 2024.
Table 2. Extended statistical analysis of the power produced by a 3 MWp PV system in May 2024.
ProbabilityPower [kW]
0.050
0.250
0.5228
0.751538
0.952499
0.5953500
0.67031000
0.83392000
0.99973000
Table 3. Results of the probability of power produced by a 3 MWp PV system in May 2024.
Table 3. Results of the probability of power produced by a 3 MWp PV system in May 2024.
Power
[kW]		Probability
≤		Probability
>
5000.59530.4047
10000.67030.3297
20000.83390.1661
30000.99970.0003
Table 4. Basic statistical analysis of the power produced by a 3 MWp PV system, after interpolation.
Table 4. Basic statistical analysis of the power produced by a 3 MWp PV system, after interpolation.
Power [kW]
Count1487
Minimum0
Maximum3188
Mean742.843
StdDev912.015
Table 5. Extended statistical analysis of the power produced by a 3 MWp PV system, after interpolation.
Table 5. Extended statistical analysis of the power produced by a 3 MWp PV system, after interpolation.
ProbabilityPower [kW]
0.050
0.250
0.5227
0.751544
0.952496
0.5958500
0.67591000
0.83592000
0.99933000
Table 6. Results of the probability of power production of a 3 MWp photovoltaic system in May 2024, after interpolation.
Table 6. Results of the probability of power production of a 3 MWp photovoltaic system in May 2024, after interpolation.
Power
[kW]		Probability
≤		Probability
>
5000.59580.4042
10000.67590.3241
20000.83590.1641
30000.99930.0007
Table 7. Results of the probability of obtaining a power greater than the assumed power levels for a 3 MWp PV system before and after interpolation.
Table 7. Results of the probability of obtaining a power greater than the assumed power levels for a 3 MWp PV system before and after interpolation.
Power
[kW]		Probability before Interpolation
> 		Probability after Interpolation
> 		Relative Error
[%]
5000.40470.40420.13
10000.32970.32411.70
20000.16610.16411.18
30000.00030.0007−100.07
Table 8. Basic statistical analysis of the power generated by a 3.45 MW wind turbine in May 2016.
Table 8. Basic statistical analysis of the power generated by a 3.45 MW wind turbine in May 2016.
Power [kW]
Count4463
Minimum0
Maximum3450
Mean980.951
StdDev911.637
Table 9. Extended statistical analysis of the power generated by a 3.45 MW wind turbine in May 2016.
Table 9. Extended statistical analysis of the power generated by a 3.45 MW wind turbine in May 2016.
ProbabilityPower [kW]
0.050
0.25221
0.5712
0.751542
0.952887
0.3979500
0.60591000
0.84022000
0.96173000
Table 10. Results of the probability of power production by a 3.45 MW wind turbine in May 2016.
Table 10. Results of the probability of power production by a 3.45 MW wind turbine in May 2016.
Power
[kW]		Probability
≤		Probability
>
5000.39790.6021
10000.60590.3941
20000.84020.1598
30000.96170.0383
Table 11. Basic statistical analysis of the power generated by a 3.45 MW wind turbine in May 2016, after interpolation.
Table 11. Basic statistical analysis of the power generated by a 3.45 MW wind turbine in May 2016, after interpolation.
Power [kW]
Count1487
Minimum0
Maximum3450
Mean978.703
StdDev906.256
Table 12. Extended statistical analysis of the power generated by a 3.45 MW wind turbine in May 2016, after interpolation.
Table 12. Extended statistical analysis of the power generated by a 3.45 MW wind turbine in May 2016, after interpolation.
ProbabilityPower [kW]
0.050
0.25225
0.5714
0.751527
0.952862
0.3907500
0.60861000
0.84672000
0.96033000
Table 13. Results of the probability of power production of a 3.45 MW wind turbine, after interpolation.
Table 13. Results of the probability of power production of a 3.45 MW wind turbine, after interpolation.
Power
[kW]		Probability
≤		Probability
>
5000.39070.6093
10000.60860.3914
20000.84670.1533
30000.96030.0397
Table 14. Results of the probability of obtaining a power greater than the assumed power levels for a wind turbine with a maximum power of 3.45 MW, before and after interpolation.
Table 14. Results of the probability of obtaining a power greater than the assumed power levels for a wind turbine with a maximum power of 3.45 MW, before and after interpolation.
Power
[kW]		Probability before Interpolation
> 		Probability after Interpolation
> 		Relative Error
[%]
5000.60210.6093−1.20
10000.39410.39140.69
20000.15980.15334.02
30000.03830.0397−3.55
Table 15. Basic statistical analysis of the power generated by the 3 MWp PV system and the 3.45 MW wind turbine in the month of May.
Table 15. Basic statistical analysis of the power generated by the 3 MWp PV system and the 3.45 MW wind turbine in the month of May.
Power [kW]
Count1487
Minimum0
Maximum6032
Mean1721.55
StdDev1142.87
Table 16. Extended statistical analysis of the power generated by the 3 MWp photovoltaic system and the 3.45 MW wind turbine in the month of May.
Table 16. Extended statistical analysis of the power generated by the 3 MWp photovoltaic system and the 3.45 MW wind turbine in the month of May.
ProbabilityPower [kW]
0.05101
0.25749
0.51623
0.752548
0.953651
0.1708500
0.32411000
0.60462000
0.85073000
Table 17. Results of the probability of power production of a 3 MWp PV system and a 3.45 MW wind turbine.
Table 17. Results of the probability of power production of a 3 MWp PV system and a 3.45 MW wind turbine.
Power
[kW]		Probability
≤		Probability
>
5000.17080.8292
10000.32410.6759
20000.60460.3954
30000.85070.1493
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Dudziak, A.; Małek, A.; Marciniak, A.; Caban, J.; Seńko, J. Probabilistic Analysis of Green Hydrogen Production from a Mix of Solar and Wind Energy. Energies 2024, 17, 4387. https://doi.org/10.3390/en17174387

AMA Style

Dudziak A, Małek A, Marciniak A, Caban J, Seńko J. Probabilistic Analysis of Green Hydrogen Production from a Mix of Solar and Wind Energy. Energies. 2024; 17(17):4387. https://doi.org/10.3390/en17174387

Chicago/Turabian Style

Dudziak, Agnieszka, Arkadiusz Małek, Andrzej Marciniak, Jacek Caban, and Jarosław Seńko. 2024. "Probabilistic Analysis of Green Hydrogen Production from a Mix of Solar and Wind Energy" Energies 17, no. 17: 4387. https://doi.org/10.3390/en17174387

APA Style

Dudziak, A., Małek, A., Marciniak, A., Caban, J., & Seńko, J. (2024). Probabilistic Analysis of Green Hydrogen Production from a Mix of Solar and Wind Energy. Energies, 17(17), 4387. https://doi.org/10.3390/en17174387

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