Operational Analysis of Power Generation from a Photovoltaic–Wind Mix and Low-Emission Hydrogen Production

Abstract

Low-emission hydrogen generation systems require large amounts of energy from renewable energy sources. This article characterizes the production of low-emission hydrogen, emphasizing its scale and the necessity for its continuity. For hydrogen production defined in this way, it is possible to select the appropriate renewable energy sources. The research part of the article presents a case study of the continuous production of large amounts of hydrogen. Daily production capacities correspond to the demand for the production of industrial chemicals and artificial fertilizers or for fueling a fleet of hydrogen buses. The production was placed in the Lublin region in Poland, where there is a large demand for low-emission hydrogen and where there are favorable conditions for the production of energy from a photovoltaic–wind mix. Statistical and probabilistic analyses were performed related to the generation of power by a photovoltaic system with a peak power of 3.45 MWp and a wind turbine with an identical maximum power. The conducted research confirmed the complementarity and substitutability relationship between one source and another within the energy mix. Then, unsupervised clustering was applied using the k-Means algorithm to divide the state space generated in the power mix. The clustering results were used to perform an operational analysis of the low-emission hydrogen generation system from a renewable energy sources mix. In the analyzed month of April, 25% of the energy generated in the photovoltaic–wind mix came from the photovoltaic system. The low-emission hydrogen generation process was in states (clusters), ensuring that the operation of the electrolyzer with nominal power amounted to 57% of the total operating time in that month. In May, the share of photovoltaics in the generated power was 45%. The low-emission hydrogen generation process was in states, ensuring that the operation of the electrolyzer with nominal power amounted to 43% of the total time in that month. In the remaining states of the hydrogen generation process, the power must be drawn from the energy storage system. The cluster analysis also showed the functioning of the operating states of the power generation process from the mix, which ensures the charging of the energy storage. The conducted research and analyses can be employed in planning and implementing effective climate and energy transformations in large companies using low-emission hydrogen.

1. Introduction

The climate and energy transformation of the European and global economies requires efficient low-emission hydrogen production systems and large amounts of cheap energy from renewable energy sources (RESs) [1]. The generation of low-emission hydrogen from RESs represents a significant domain for the implementation of the latest techniques for diverse hydrogen production and its storage, transport [2], and distribution [3]. Equally substantial challenges face those who will provide electricity to the large hydrogen plants. This issue includes the creation of policies favoring energy production from RESs [4] and the physical implementation of modern power lines [5]. Especially during the implementation of innovative technologies, they should be subject to detailed monitoring in order to track the correctness of the processes taking place and to ensure safety [6]. All components in the system should be Internet of Things (IoT) devices, and the large measurement data obtained from them (Big data) should be analyzed and processed using traditional and artificial intelligence (AI) algorithms [7]. Such operational analysis will enable the effective optimization of individual system components [8] and, in the future, it will be the basis for the development and implementation of advanced process control (APC) [9]. The entire approach to the production of low-emission hydrogen from RESs must be carried out with the active participation of scientists who will research and develop both individual algorithms and entire tools for optimizing and controlling the production processes of both electricity [10] and hydrogen itself [11].

The process of producing low-emission hydrogen using renewable energy sources is complex and requires detailed analysis in each specific application [12,13]. As with any complex process, it can be decomposed into a series of simpler processes. These, in turn, are easier to analyze for optimization purposes and the development of effective control [14]. In the intricate process of producing low-emission hydrogen through renewable energy sources, the purpose of hydrogen production is of paramount importance [15]. For this reason, the demand for hydrogen can be divided into the following groups:

• Continuous production of small amounts of hydrogen (up to several kilograms per day) without the need for its compression. It is used in continuous food and industrial production processes with low demand for hydrogen [16].
• Continuous production of small amounts of hydrogen (up to several kilograms per day) with the need to compress it to 700 bar and store it. It is used in hydrogen production processes for the purpose of powering passenger cars with hydrogen fuel cells [17].
• Continuous production of medium amounts of hydrogen (up to several hundred kilograms per day) without the need for its compression. It is used in continuous food and industrial production processes with a medium demand for hydrogen.
• Continuous production of medium amounts of hydrogen (up to several hundred kilograms per day) with the need for its compression to 350 bar and storage. It is used in hydrogen production processes for the purpose of powering buses with hydrogen fuel cells [18].
• Continuous production of large amounts of hydrogen (up to several tons per day) without the need for its compression. It is used in continuous production processes of industrial chemicals [19] and artificial fertilizers with high demand for hydrogen [20].
• Continuous production of large amounts of hydrogen (up to several tons per day) with the need for its compression to 350 bar and 700 bar, and storage. It is used in hydrogen production processes for the purpose of powering fleets of buses, passenger cars, and delivery vehicles with hydrogen fuel cells [21].
• Discontinuous hydrogen production as a medium for storing surplus production from renewable energy sources (from several to several hundred kilograms per day) with the need to compress it to 350 bar and 700 bar and store it [22]. It is used in hydrogen production processes for the purpose of powering vehicles and home systems, generating heat and electricity based on stationary fuel cells [23].

In this article, the authors assume the use of low-emission hydrogen for the production of artificial fertilizers [24] or industrial chemicals [25]. Until now, gray hydrogen produced in the processes of steam reforming of natural gas has been used for its production [26]. Control of such large and complex production processes is currently carried out using the APC (advanced process control) formula. An important reason for selecting such a hydrogen production target is its substantial demand, which can reach tons of hydrogen per day [27]. Another requirement is the continuous production of hydrogen due to the integration of its production with other substrates needed for the production of artificial fertilizers [28]. The hydrogen production process must, therefore, be continuous, and it is rather difficult to provide large amounts of stored hydrogen to support the production processes. Stationary storage of tons of hydrogen in compressed, cryogenic, or metal hydride form is simply not economically viable. Due to these difficulties, there is a growing preference for the production of green ammonia as opposed to hydrogen in its purest form [29,30]. The only option that can be considered is to regulate the efficiency of hydrogen production, to which the rest of the partial processes that make up the overall process of producing artificial fertilizers can be adapted. The continuity of demand for hydrogen in a given location can also be supported by its supply via hydrogen pipelines [31]. At the same time, they constitute a hydrogen storage facility, but the costs of their construction are enormous [32].

It is important to note that the production of low-emission hydrogen should not disrupt or burden existing receivers of energy from renewable energy sources [33]. Therefore, low-emission hydrogen production systems should be powered by newly created capacities from renewable energy sources [34]. All sources generating energy in renewable energy mixes should also be subjected to a detailed characterization and analysis [35]. According to the authors, it is imperative to know and quantitatively describe the substitutability and supplementation of energy production by individual sources within the energy mix [36]. Another essential element of energy generation for the production of low-emission hydrogen is the need to use energy storage systems with large energy capacities [37,38]. They are needed to store the surplus energy produced in relation to the continuous demand for electrolyzer power and to release it at times of lower energy production [39]. At present, they are the most cost-effective methods of enabling self-balancing of the newly created generating capacities from renewable energy sources [40]. In the previous articles, the authors have already shown that with the appropriate design of power generation from individual renewable energy sources, the size of the energy storage does not have to be very large at all.

The Internet of Things (IoT) has become a prominent phenomenon in the third decade of the 21st century [41]. The IoT is a concept in which everyday devices are connected to the Internet, enabling them to communicate with each other and with their users. Due to the integration of sensors and software, devices such as refrigerators, cars, or smart watches can collect, analyze, and transmit data in real time. This allows for the automation of many processes, increased convenience, and optimization of resource consumption, e.g., energy. The IoT is employed in many industries, from smart homes and cities to industry, transport, and healthcare. Another salient trend present in the industry is Industry 4.0 [42]. This is a concept of modern production, which uses advanced digital technologies such as the Internet of Things (IoT), artificial intelligence, robotics, and data analysis. The objective of this initiative is to establish smart factories, in which machinery, systems, and people communicate in real time, thereby automating processes and increasing efficiency. This allows for the personalization of production, cost reduction, and resource optimization. Industry 4.0 contributes to increasing the competitiveness of companies and transforming traditional business models into more flexible and sustainable ones. In addition, artificial intelligence (AI) supports Industry 4.0 by analyzing huge amounts of data, enabling the optimization of production processes and predicting machine failures. Due to machine learning algorithms, systems can automatically adjust the operating parameters of devices, which increases efficiency and reduces losses. Advanced process control (APC) is an advanced method of controlling industrial processes that applies mathematical models and algorithms to optimize the operation of the systems [43]. APC analyzes data in real time and predicts changes in the process, enabling automatic adjustment of parameters to improve the efficiency and quality of production. This allows for reducing the consumption of raw materials, energy, and waste. This technology is adopted in various industries, such as the chemical, oil, energy, and food industries, providing better control and stability of the processes. The research conducted by the authors aligns closely with the three trends outlined above related to the acquisition and processing of large amounts of data from renewable energy sources to support business decision-making (Business Intelligence).

In recent literature, the topic of creating efficient energy mixes consisting of different renewable energy sources is very often discussed. Meister et al. analyzed how wind and PV systems can complement each other to balance power [44]. Ten years of meteorological data were used to assess annual fluctuations and calculate the demand coverage factor (DCF). The results indicated that the optimal ratio of wind to PV energy production is 0.7/0.3 or 0.8/0.2, respectively, achieving a DCF of 0.62. Meister et al. used real measurement data from wind speed measuring towers and real photovoltaic systems. The authors concluded that different scenarios related to the substitutability and supplementarity of energy production by individual RESs should be mathematically described. However, the authors also use a real case of electricity demand. In relation to the time-varying power consumption profile, the authors calculated the DCF depending on the different shares of individual RESs in the energy mix. The research was conducted using real measurement data for wind and sun conditions in Estonia and the United States. The authors also perform an analytical calculation of the required ESS.

Al-Fatlawy et al. discussed different strategies for integrating PV and wind systems to provide a sustainable and reliable power supply [45]. The proposed approaches include the use of energy storage, intelligent management systems, and optimization of the size of system components. A probabilistic power flow (PPF) analysis algorithm was developed by researchers from Iraq and India to assess the impact of uncertainties in renewable energy generation and demand in the power grid. The authors used probabilistic models based on probability density functions to represent the variability of factors such as solar irradiance, wind speed, and load behavior. The results of the probabilistic analysis presented in the paper prove that the system is able to effectively manage the fluctuations in energy generation and demand, maintaining voltage stability and ensuring reliable power flow.

Elminshawy et al. investigated the technical and economic feasibility of a stand-alone hybrid system based on photovoltaic cells, a wind turbine, an energy storage device, and a water electrolyzer to generate electricity and green hydrogen in three regions of Egypt with different climates [46]. The researchers showed that within a single country, there can be more or less favorable solar and wind conditions, which have a direct impact on the costs of electricity production and low-emission hydrogen. Such studies have great practical application, as they help authorities to design different national hydrogen production systems in different locations within a given country. It turns out that the differences in energy production by photovoltaic and wind systems in different geographical contexts are very large. The authors show that the Lublin region in Poland is a convenient location for investment in the production of electricity from a photovoltaic–wind mix and for the production of green hydrogen.

Determining the signatures of power generated in the photovoltaic–wind mix using clustering has its advantages and disadvantages compared to other scientific methods. Compared to probabilistic analysis using the Metalog probability distribution family, it allows determining the complementarity and substitutability of the power generated by one source with another. The Metalog probability distribution family allows for the calculation of the probability of generating individual power levels by the tested energy mix [6]. Unsupervised clustering does not have this possibility. The signatures of power generated by the energy mix and the presentation of their results in the form of heat maps allow the locating of time periods requiring the accumulation of overproduction of power and periods of its deficit, when power must be drawn from the power grid or energy storage systems. Clustering does not allow for the exact calculation of the size of the energy storage system. Analysis of the monthly average hourly power allows determining the size of the energy storage [7]. All presented methods for assessing the efficiency of energy mixes provide significant information about the process of generating power and energy production. They can be used simultaneously or interchangeably, depending on the needs. Markov models can be used in the analysis of energy generated from RESs in many aspects, such as forecasting [47], optimization [48], and reliability analysis [49].

In this article, the authors conduct an operational analysis of low-emission production from a photovoltaic–wind mix. The article is a response from the scientific side to the need to support entrepreneurs in the area of planning, implementing, and optimizing hydrogen production systems for the purposes of climate and energy transformation. The article is a case study of hydrogen production in the Lublin region in Poland. This research is justified by the production of industrial chemicals, fertilizers [50], and buses powered by hydrogen fuel cells in our region [51]. Each of these industries requires large amounts of cheap, low-emission hydrogen. Additionally, the Lublin region is characterized by favorable climate conditions for the production of energy from the sun and the wind on a national scale. All this contributes to the possibility of designing and creating a regional ecosystem for the production and use of low-emission hydrogen. The initial goal of the article is to characterize the production of energy from a photovoltaic–wind mix using statistical and probabilistic methods. The main objective of the article is to process the measurement data of the generated power from a photovoltaic–wind mix using unsupervised clustering methods and to demonstrate their usefulness in the operational analysis of energy generation for the production of low-emission hydrogen.

The article presents a practical method of designing and assessing the power generated in a photovoltaic–wind mix for the production of low-emission hydrogen. The authors oppose the commonly accepted statement that balancing power in a photovoltaic–wind mix is impossible or very difficult to implement in practice. The signature of the power generated in the mix depends on the power signatures of individual RESs. Therefore, the authors perform detailed statistical analyses and clustering of individual RESs and then their mix. The authors prove quantitatively that individual RESs in the mix replace and complement each other. Importantly, the Probability Density Function of the power generated in the mix in one of the months shows characteristics of anti-fragile systems. This means that designing a photovoltaic–wind mix is possible in this direction in more months of the year. Such an indicator of the efficiency of the energy mix has not been used so far in science and in industrial practice. Signatures of generated power in the photovoltaic–wind mix were prepared using unsupervised clustering. Individual states of the power generation process in the mix were given a physical meaning related to the quality of generated power and the related possibilities of producing low-emission hydrogen. This approach is called operational analysis and, according to the authors, is necessary to understand the nature of each RES and its mix. Operational analysis based on signatures determined as a result of clustering allows for the identification of the occurrence of the process in selected clusters in individual time intervals over the course of a good. The authors present a very detailed analysis of the generated power by individual RESs and their mix using traditional statistical tools and modern algorithms for processing measurement data.

2. Materials and Methods

The authors used the KNIME (Konstanz Information Miner) Analytics Platform version 5.3.2 in their research [52]. It is used in processing measurement data by integrating, cleaning, and transforming large sets of measurement data from different sources. In scientific research, it enables statistical analysis, modeling, and visualization of results, which supports data interpretation. Because of its modular structure, it allows for building complex workflows without the need for programming, which is particularly useful for scientists from various fields. KNIME also supports machine learning and data mining, which facilitates the identification of patterns and relationships in measurement data. Additionally, it enables the automation of analytical processes, which increases the efficiency and repeatability of research.

The appearance of the dialog window in the KNIME Analytics Platform and the acquisition and processing of measurement data in the graphical programming language are shown in Figure 1.

The operational analysis of the power generation from the photovoltaic–wind mix and the production of low-emission hydrogen will include the identification and description of individual processes that can have practical applications in the optimization of the entire complex process. For this purpose, the unsupervised clustering method using the k-Means algorithm is used [53]. Unsupervised k-Means clustering allows for grouping measurement data without the need for prior labeling, which is useful when there are no labeled examples [54]. This method facilitates identification of the hidden patterns and structures in the data, which can lead to new, non-obvious conclusions [55]. Unlike supervised algorithms, k-Means does not require large training sets, which reduces the cost and time of the data preparation [56]. Due to its simplicity and scalability, it is well suited for analyzing large data sets, e.g., in customer segmentation or anomaly detection [57]. The k-Means algorithm is often used as a preliminary step for further analysis, e.g., to reduce dimensionality [58] or improve the performance of supervised algorithms [59].

3. Characterization of Measurement Data and Statistical Analysis

This chapter focuses on the measurement data from the photovoltaic system and the wind turbine. A preliminary characterization of the individual energy sources separately and their mix is also performed. A low-emission hydrogen production system based on water electrolysis (hydrolysis) is also characterized. Quantitatively significant data is provided by the statistical analyses and histograms of the generated power density.

3.1. Characteristics of the Photovoltaic System

The data characterizing the energy generation by the photovoltaic systems were obtained from a system with a peak power of 5.85 kWp located a short distance from the city of Lublin. The data were made available by the owner of the photovoltaic system on the Internet platform of the manufacturer of the photovoltaic inverters SolarEdge. Every Internet user can obtain and process this type of data pertaining to the power generation during the day and the amount of energy produced daily, weekly, annually, or in a selected period of time. The data obtained from a system with a peak power of 5.85 kWp were scaled to a peak power of 3.45 MWp, which corresponds to the maximum power of the wind turbine used. In a previous publication, the authors demonstrated a strong correlation between the generated power and energy produced by systems with a peak power of several kW and several dozen kW. The time series of the generated power was recorded every 30 min for the entire month of April, and it is presented in Figure 2. The time series, therefore, contains 1440 records. The graph clearly depicts the cyclical nature of power generation from the photovoltaic system during the day and night. Interestingly, the graph vividly illustrates that the maximum power generated by the photovoltaic system at noon is higher in April than in May. This happens despite the fact that in May the sun rises higher above the horizon than in April. However, April is a much colder month than May, which has a positive effect on the efficiency of the photovoltaic system and on the greater power generated.

3.2. Characteristics of a Wind Turbine

Measurement data characterizing the power generated by the wind turbine were also obtained in real conditions. Wind speed was measured using a measuring tower. The tower was set up in the Lublin region in Poland and took continuous measurements for a period of 2 years. The average measurement data from 4 anemometers located at different heights of the tower were sent every 10 min. It should be noted that a wind turbine is currently operational at the location of the measuring tower. The measured wind speeds combined with the power characteristics of the Vestas 126 turbine with a maximum power of 3.45 Mw with a rotor placed at a height of 140 m allowed obtaining the course of generated power over time. The time series of the power generated by the wind turbine with a maximum power of 3.45 MW in April and May is presented in Figure 3. The average wind speed in April was 7.731 m/s, which allowed the turbine to generate an average power of 1467 kW. The turbine, working for 720 h, produced 1,091,354 kWh of energy. The calculated power factor was 44%. The average wind speed in May was 6.39 m/s, which allowed the turbine to generate an average power of 939 kW. The turbine, working for 744 h, produced 698,351 kWh of energy. The calculated power factor was 27%. Therefore, April can be regarded as a favorable month with regard to wind energy production, while May can be considered average.

3.3. Preliminary Characterization of the Photovoltaic–Wind Mix

Figure 4 depicts the time series of the course of the generated power by the photovoltaic system, the wind turbine, and their mix in the month of May. It can be seen that RESs both replace and complement each other. The replacement is clearly visible at night since the photovoltaic system does not generate any energy at that time. The only supplier of power to the mix is the wind turbine. The moments when the wind turbine is not operating are not apparent on the graph, and the only supplier of energy to the mix is the photovoltaic system. As mentioned earlier, April in the Lublin climate and geographical conditions is usually windy and is a very good month for wind energy production. The time series shows periods corresponding to the operation of the wind turbine with maximum power. As can be seen from the characteristics of the Vestas 126 3.45 MW wind turbine, it generates maximum power at wind speeds of 12 m/s and more.

In the mix time series, there are moments when different RESs complement each other in generating power. There are also several peaks in which the generated power exceeds 5000 kW.

Despite many differences in the power generated by the photovoltaic system and the wind turbine in April and May, many common features can also be seen. May is also dominated by moments in which the individual power sources in the mix complement each other. Several peaks with power greater than 5000 kW can also be observed in the course of the mix, which is visible in the graph in Figure 5. Close observation of the mix time series in April and May suggests the idea of powering hydrogen electrolyzers with a power of 2000 kW. Of course, the process of achieving such a continuous level of power generation on the scale of both months must include the use of an energy storage system (ESS). It will be charged with the excess generated power and discharged when the mix generates a lower power level than assumed.

A lot of information about the process of generating power from the photovoltaic system, the wind turbine, and their energy mix is provided by statistical analysis. Its results for April are presented in

Table 1. Statistical data of generated power from photovoltaic system, wind turbine, and their mix in the month of April.

Name	Minimum	Maximum	25% Quantile	50% Quantile	75% Quantile	Mean	Mean Absolute Deviation	Standard Deviation	Sum
Pwind (kW)	0.0	3450.0	546.25	1309.5	2390.25	1508.5	933.3	1082.8	2,172,248.0
Ppv (kW)	0.0	2971.0	0.0	70.0	798.75	527.9	622.6	789.5	760,190.0
Pmix (kW)	0.0	6267.0	1001.75	1826.5	2941.5	2036.4	1083.5	1314.3	2,932,430.0

, and for May in

Table 2. Statistical data of generated power from photovoltaic system, wind turbine, and their mix in the month of May.

Name	Minimum	Maximum	25% Quantile	50% Quantile	75% Quantile	Mean	Mean Absolute Deviation	Standard Deviation	Sum
Pwind (kW)	0.0	3450.0	214.0	653.5	1428.0	939.0	734.6	917.3	1,397,247.0
Ppv (kW)	0.0	2917.0	0.0	169.5	1665.0	797.8	873.0	986.1	1,187,075.0
Pmix (kW)	0.0	6216.0	712.25	1578.5	2576.0	1736.8	990.9	1214.7	2,584,324.0

. From the presented data, we can read the average monthly power generated by the individual RES. Quantile values provide important quantitative input about the probability of generating power lower/equal to/higher than the specified percentage thresholds. From the comparison of statistical data in both months, direct conclusions can be drawn about the amount of energy produced by individual renewable sources and their mix. The presented data facilitates the calculation of the monthly share of power generated by the photovoltaic system and the wind turbine. The calculations show that in April only about 25% of the energy produced in the mix came from the photovoltaic system. In May, the share of photovoltaics in the generated power was about 45%. Such a large difference from month to month in the share of individual RESs in the mix indicates a high variability of the power generation processes and energy production by individual RES.

Figure 6 presents the histogram of the probability density of power generation by the photovoltaic system, wind turbine, and their mix in April and May. In the case of the photovoltaic system, the dominant density value is the one encompassing zero and close to it. This indicates that a significant portion of the photovoltaic system’s total power generation deficit occurs at night. A comparison of the density of power generated by the photovoltaic system in May compared to April indicates a significant increase in power generation in the high power ranges. In the case of the probability density of power generated by the wind turbine, the situation is the opposite. April was a much more stable month in terms of power generation from the wind. Interestingly, in April, the Probability Density Function will be bimodal. This results from the fact that there is a high density for the maximum range of power generated by the turbine.

The monthly comparison of the histograms for the photovoltaic–wind mix leads to noteworthy conclusions. They clearly show that individual renewable sources replace and complement each other. The histogram for the energy mix in April is of particular interest. Its shape is characteristic of the so-called antifragile systems. These are the characteristic systems that are not only resistant to variability and stressors, but actually benefit from them, strengthening in difficult conditions. This concept was introduced by Nassim Nicholas Taleb and refers to biological, economic, or organizational systems that develop due to unpredictability [60]. In practice, this means designing organizations, strategies, or technologies in such a way that they benefit from uncertainty, errors, and disruptions. The photovoltaic–wind mix can be considered an antifragile system because it benefits from dynamic and unpredictable weather conditions, which are a problem in traditional energy systems. The variability of sunlight and wind force means that these energy sources complement each other, i.e., if there is no wind, the sun often shines, and if there is a lack of sun, the wind can generate the energy. With the development of energy storage technology and smart grids, this system not only gains resistance to disruptions but also strengthens in difficult conditions, e.g., when the demand increases or during extreme weather conditions. This mix also allows for better adaptation to changes in the power grid and dynamic response to demand, which increases energy stability and independence. As a result, the system will not only survive in difficult conditions but will also develop and adapt to changing circumstances, which is in line with the idea of antifragility.

3.4. Hydrogen Production Characteristics

A visit by one of the authors to the hydrogen fairs in Bremen (Germany) and Paris (France) confirmed that there are many methods of producing hydrogen [61]. However, they have been developed to different technology readiness levels (TRLs). Electrolytic methods used for water hydrolysis are currently the most advanced and ready for mass production and market implementation [62]. Among them, a new type of electrolyzer with anion exchange membrane (AEM) should be mentioned [63]. AEM hydrogen electrolyzers are increasingly used to produce green hydrogen from the energy from renewable sources [64]. Their design allows for effective cooperation with unstable power sources, characteristic of renewable sources, such as solar or wind energy. Due to the use of anion exchange membranes, these electrolyzers can operate in dynamic conditions [65]. Therefore, this indicates the ability to quickly adapt to the changing power conditions without significant loss of efficiency. This characteristic renders them particularly suitable for integration with renewable energy systems, where fluctuations in energy availability are prevalent.

Compared to the traditional alkaline electrolyzers, AEM electrolyzers are characterized by a simpler and more compact design, which facilitates their use in a variety of applications. However, it is important to acknowledge their shorter lifetime compared to other electrolysis technologies. This can affect the long-term efficiency of the system and should be taken into account both in cost calculations and in maintenance planning.

In practice, the stability of the power supply of AEM electrolyzers from renewable energy can be further improved by using some energy storage systems, such as batteries or supercapacitors, which assist to smooth out short-term power fluctuations. Such solutions allow for more stable and continuous operation of the electrolyzers, even in conditions of variable energy production from renewable energy.

Enapter’s Nexus electrolyzer (shown in Figure 7) is a modular megawatt-scale green hydrogen production device, available in 500 kW and 1 MW capacities [60]. Enapter is a technology company offering AEM electrolyzers headquartered in Saerbeck, Germany. The 1 MW model (AEM Nexus 1000 made by Enapter) produces up to 210 Nm³ of hydrogen per hour, equivalent to 450 kg per day, with an energy consumption of approximately 53.3 kWh per kilogram of hydrogen. It provides hydrogen purity of 99.95%, with the potential to reach 99.999% with an optional dryer, and an output pressure of up to 35 bar. With its modular design, consisting of hundreds of AEM electrolyzer cores, the Nexus offers high reliability and operational flexibility from 3% to 100% load, enabling the efficient use of variable renewable energy sources. Additionally, the design allows for individual sections to operate independently, ensuring continuous hydrogen production even during the servicing of some modules.

The production of low-emission hydrogen from renewable energy sources requires an effective connection of systems with different operating characteristics. A photovoltaic system generates direct current (DC), while a wind turbine usually supplies alternating current (AC). Hydrogen electrolyzers, especially PEM (proton exchange membrane) types, require a DC power supply with stable parameters. Proper connection requires the use of appropriate energy conversion and power management systems. In the basic system, the photovoltaic panel is connected to a DC/DC converter with the MPPT (maximum power point tracking) function, which ensures PV operation at the optimal point and stabilizes the output voltage. In turn, a wind turbine generating alternating current (usually three-phase) must be connected to an AC/DC rectifier. After the rectifier, it is recommended to use a DC/DC converter, which adapts the wind voltage to the requirements of a common DC bus. Both sources, after appropriate conversion, are connected on a common DC bus. This bus supplies the electrolyzer. In more advanced systems, additional buffering systems (batteries or supercapacitors) are used to compensate for short-term power fluctuations and ensure stable operating conditions for the electrolyzer. Key design challenges include:

• compatibility of source voltages with electrolyzer requirements,
• management of variability of power generated by PV and wind,
• minimization of energy losses in conversion stages,
• ensuring operational safety through overvoltage and overload protection systems.

4. Discussion

One of the computational nodes in KNIME is the Silhouette Coefficient. It allows us to evaluate the clustering quality by determining how well elements fit into their clusters compared to other groups. The coefficient value ranges from −1 to 1, where higher values indicate a better fit of points to their own clusters and their greater separation from others. This metric facilitates the comparison of different clustering results, thereby assisting in the selection of the optimal number of clusters in algorithms such as k-means. It is especially beneficial in exploratory data analysis when there are no known class labels, because it provides an intuitive way to assess the coherence of groups. By means of the Silhouette Coefficient [67], one can avoid both too many (by over-splitting) and too few (by merging unrelated elements) clusters. The results of the average Silhouette Coefficient values for different numbers of clusters for the month of April are presented in

Table 3. Mean Silhouette Coefficient for division into different numbers of clusters for April.

Cluster_Number	Mean Silhouette Coefficient
Cluster_0	0.31	0.26	0.23	0.41	0.40	0.41	0.40	0.45	0.45
Cluster_1	0.43	0.53	0.52	0.58	0.55	0.44	0.41	0.37	0.43
Cluster_2		0.58	0.50	0.44	0.50	0.46	0.40	0.42	0.38
Cluster_3			0.46	0.52	0.44	0.55	0.21	0.31	0.47
Cluster_4				0.43	0.46	0.45	0.48	0.32	0.29
Cluster_5					0.38	0.21	0.45	0.47	0.34
Cluster_6						0.53	0.50	0.42	0.44
Cluster_7							0.42	0.52	0.42
Cluster_8								0.41	0.50
Cluster_9									0.30
Overall	0.41	0.51	0.45	0.49	0.45	0.46	0.42	0.43	0.41

, and for the month of May in

Table 4. Mean Silhouette Coefficient for division into different numbers of clusters for May.

Cluster_Number	Mean Silhouette Coefficient
Cluster_0	0.50	0.59	0.55	0.49	0.46	0.45	0.45	0.49	0.50
Cluster_1	0.50	0.47	0.39	0.54	0.58	0.55	0.61	0.6	0.59
Cluster_2		0.46	0.47	0.28	0.53	0.53	0.49	0.52	0.61
Cluster_3			0.26	0.47	0.32	0.29	0.30	0.36	0.40
Cluster_4				0.52	0.48	0.26	0.25	0.27	0.25
Cluster_5					0.50	0.51	0.46	0.47	0.46
Cluster_6						0.44	0.44	0.43	0.52
Cluster_7							0.44	0.41	0.44
Cluster_8								0.40	0.38
Cluster_9									0.40
Overall	0.50	0.52	0.45	0.48	0.50	0.46	0.45	0.46	0.46

. The highest Silhouette Coefficient value for both months was obtained for the number of clusters equal to 3 (red font in Table 3 and Table 4). It should be noted that for other numbers of clusters the Silhouette Coefficient is also very high and changes only slightly. In this case, the choice of the number of clusters is left to the expert’s discretion. The number of clusters will be adjusted to the number of process states that can be named and used in the management of low-emission hydrogen production.

The unsupervised clustering process was initiated based on the determined Silhouette Coefficient values. The two-dimensional state space was divided into three clusters. The clustering results for April are shown in Figure 8a, and for May in Figure 8b. Despite some similarities, the division of the generated power space has clear differences. These are the boundary differences in the generated power. For example, cluster_0 (red) in May seems to be separated by a horizontal boundary of about 1300 kW on the wind power axis and a vertical boundary of 1200 kW on the photovoltaic power axis. Unlike in May, cluster_2 (red) has a completely different shape in April. It has a clear horizontal boundary of about 1700 kW on the wind power axis. However, the boundary separating it from cluster_0 (green) is not vertical. Cluster_2 (red) clearly cuts into cluster_0 (green) at the bottom. Similar observations can be made by carefully looking at the division boundaries between all clusters. The authors decided that the division into 3 clusters is not sufficient to describe the production of low-emission hydrogen. The spaces of generated power defined by 3 clusters are too large and may contain many potential characteristic substates. In this case, the authors decided to decompose and divide the generated power space into 6 clusters. The reason for this choice was the high Silhouette Coefficient of 0.5 for the month of May.

The clustering results into 6 clusters for April are shown in Figure 9a, and for May in Figure 9b. Also with this division, despite certain similarities, the division of the generated power space has clear differences. For April, the k-Means algorithm divided it into 4 clusters along the turbine power axis and only into 2 clusters along the photovoltaic power axis. For May, the division was the opposite. The k-Means algorithm divided it into 3 clusters along the turbine power axis and into 3 clusters along the photovoltaic power axis. This division has its mathematical explanation. It results from the statistics and histograms presented in Table 1 and Table 2 and in Figure 6. A larger number of records in a given range of generated power forces the generation of a larger number of clusters in that range. The authors considered that the division into 6 clusters is also not sufficient to describe the production of low-emission hydrogen. The generated power spaces designated by 6 clusters are too large and may contain many potential characteristic substates. In this case, the authors decided to decompose and divide the generated power space into 9 clusters. The reason for this choice was the high Silhouette Coefficient for both months. Both for April and May, the Silhouette Coefficient for the division into 9 clusters was higher than for the neighboring values.

The results of clustering into 9 clusters for the month of April are presented in Figure 10a and for the month of May in Figure 10b. Expert verification of the obtained clustering results for April is presented in

Table 5. Expert validation of the obtained clustering results for the month of April.

Cluster Number	Cluster Color	Cluster Physical Meaning
0	light blue	very low PV, medium WIND, normal H2
1	green	medium-very high PV, medium-very high WIND, normal H2 + ESS charging
2	blue	very low PV, high WIND, normal H2 + ESS charging
3	violet	very low-low PV, low-medium WIND, normal H2 + ESS charging
4	yellow	low-medium PV, very low-low WIND, reduced-normal H2, ESS discharging
5	brown	very low-low PV, very high WIND, normal H2 + ESS charging
6	orange	high-very high PV, very low-low WIND, normal H2 + ESS charging
7	red	very low PV, very low WIND, reduced-normal H2, ESS discharging
8	pink	very low PV, low WIND, reduced-normal H2, ESS discharging

and for May in

Table 6. Expert validation of the obtained clustering results for the month of May.

Cluster Number	Cluster Color	Cluster Physical Meaning
0	green	medium-very high PV, medium-very high WIND, normal H2 + ESS charging
1	red	very low PV, very low WIND, reduced-normal H2, ESS discharging
2	brown	very low-low PV, high-very high WIND, normal H2 + ESS charging
3	yellow	low-medium PV, very low-low WIND, reduced-normal H2, ESS discharging
4	violet	very low-low PV, low-medium WIND, normal H2 + ESS charging
5	blue	very low-low PV, medium WIND, normal H2
6	pink	very low PV, low WIND, reduced-normal H2, ESS discharging
7	mauve	medium-high PV, very low-low WIND, reduced-normal H2 + ESS charging
8	orange	high-very high PV, very low-low WIND, normal H2 + ESS charging

.

After the clustering process, the results can be presented in the form of state-transition diagrams. Figure 11 shows the state-transition diagram for May 1. It is possible to track the process of generating power from the photovoltaic–wind mix in individual periods of the day. It is clearly visible that the process very often stays in a given state (cluster) for only half an hour. Usually, it stays in it for 2, 3, 4, or more such half-hour periods. Further statistical or probabilistic analysis can also be used for transitions from one state to another. Learning such process behaviors with accuracy to the probability distribution can have practical application in predicting such complex processes.

Very important data in terms of quantity is provided by the monthly analysis of the relative frequency of the power generation process in individual states (clusters). The relative frequency of the power generation process in individual clusters (divided into 9 clusters) in individual months is presented in Figure 12. At this time, it is imperative to recall that the division into 9 clusters during the period of April and May corresponds to the data presented in Figure 10. However, the clusters obtained in these months are not identical and should not be compared in terms of colors or cluster numbers. Taking into account the division into an equal number of clusters (9) and a very similar clustering quality obtained in individual clusters as well as its average value for all clusters, a certain observation can be made, i.e., the process of generating power by the photovoltaic–wind mix in the individual months of April and May is characterized by a certain similarity.

The next stage of cluster analysis involves drawing up graphs of the process occurrence in individual clusters in specific hourly intervals. The calculation data presented in Figure 13 show that the process presence in individual clusters usually occurs at the same times of day. Analyzing the data from both April and May, one can conclude that the generation of power from the photovoltaic–wind mix is repetitive in a daily perspective.

The most obvious example of daily repeatability (cyclicality) of the occurrence of the process of generating power from the RES mix is the daily generation of power by the photovoltaic system. The corresponding cluster_6 in April and cluster_8 in May clearly occur during the day. Another example is the generation of average power by a wind turbine. This is the state of cluster_2 in April and cluster_5 in May. For May, it can be seen that this type of state does not occur during the day. For April, the break during the day is smaller because this cluster also includes the generation of power from the photovoltaic system, with values up to several hundred kW.

Heatmaps undoubtedly provide the most quantitative information on the occurrence of clustering over time. They are a graphical representation of the data in which numerical values are presented using colors, making it easier to identify patterns and trends. They are used, among others, in website traffic analysis, UX research, and statistical data visualization. They can be used to quickly see which areas are most frequently used, clicked, or viewed. Heatmaps add a third dimension to a two-dimensional graph by representing numerical values using colors, which makes it easier to analyze complex data. This enables the simultaneous visualization of the relationships between two variables and the intensity of their values at different points on the graph. Heatmaps for the clustering results of power generation processes from the photovoltaic–wind mix in April and May are presented in Figure 14.

The practical use of heatmaps will be presented to analyze the most important cases related to the production of low-emission hydrogen from a photovoltaic–wind mix. The first case is associated with a large overproduction of generated power and energy produced from the mix, which significantly exceeds the maximum power threshold of the hydrogen electrolyzers used. In the case of April, this process corresponds to cluster_1 (green), and in the case of May, cluster_0 (green). The heatmap shows that this condition occurs in April only during the day, with a fairly high frequency of occurrence. In May, this condition also occurs only during the day, but with a much lower frequency. Let us recall that this condition corresponds to the generation of power by both renewable sources with a total power exceeding 3500 kW. It also includes powers exceeding 6000 kW. This means the need to promote large amounts of energy, constituting overproduction in relation to the assumed level of electrolyzer power of 2000 kW. However, not only do the above-mentioned clusters require energy storage, but the need to store large amounts of energy is also necessary in the process states in which high levels of total mix power result from high power generated mostly by one source. Consider the first case, when high total mix power is obtained largely from the photovoltaic system. This corresponds to the cluster_6 state in April and cluster_8 in May. Both clusters occur in the middle of the day with high frequency. However, the frequency of this state in May is much higher than in April due to the higher share of photovoltaic power in the mix. The total power generated in this state by both sources ranges from 2000 to 4000 kW in both months. The second case of generating a high level of total mix power results from the higher share of wind power in the mix. In April, this process corresponds to cluster_5 and in May to cluster_2. In April, cluster_5 occurs throughout the day, but its frequency is the highest at night after midnight. In May, cluster_2 occurs clearly at night, both before and after midnight. The total power generated in this state by both sources is between 3000 and 4000 kW in both months.

After analyzing the overproduction of energy from the photovoltaic mix, it was time to analyze the power shortages in relation to the assumed level of electrolyzer power. Heatmaps prove to be a valuable solution in this area as well. The state of the lowest generated power from both RESs corresponds to cluster_7 in April and cluster_1 in May. Both clusters are very similar in terms of their boundaries. They cover the power range from 0 to over 1000 kW. It is evident that this is insufficient to generate the requisite electrical power necessary to facilitate the electrolysis process. During this state, power must be supplied to the electrolytic processes from previously charged energy storage. It is worth noting here that red clusters have the highest frequency of occurrence in both months, amounting to 19% and 22%, respectively (see Figure 12). Cluster_7 in April occurs with the highest frequency in the morning and evening hours. Similar frequencies of occurrence are visible for cluster_1 in May. Despite the highest frequencies occurring in the morning and evening hours, attention should be paid to their occurrence throughout the night in both months analyzed.

From the analysis presented above, a number of noteworthy conclusions can be drawn in the area of balancing the power generation system from the photovoltaic–wind mix and the production of low-emission hydrogen. In both analyzed months, there is a morning and evening minimum of power generation from the RES mix. In both analyzed months, there is a night and afternoon maximum of power generation from the RES mix. This allows the energy storage system to be charged from night overproduction and then discharged during the morning minimum. Then, at noon, the ESS will be charged again with the energy from the afternoon overproduction to make up for the shortages during the evening minimum. Therefore, on the majority of days in the analyzed months, the ESS will be charged and discharged twice a day. The conducted clustering shows that the ESS will be charged from the excess energy produced in the hydrogen production system during the periods when the energy is the cheapest. The conducted clustering shows that the ESS will be discharged during the periods when the energy purchased from the power grid is the most expensive. This means that such a system of producing energy from a mix of renewable energy sources for the production of low-emission hydrogen can be optimized in terms of electricity costs, which will positively affect the cost of hydrogen production.

The approach, methodology, and IT tools used by the authors have some limitations. Despite indicating very specific periods of overproduction of power by RESs and power shortages in the low-emission hydrogen production system, no results were obtained in the form of ESS capacity. This means that such a complex issue as the production of low-emission hydrogen from a photovoltaic–wind mix must use many different scientific methodologies and tools. The approach used by the authors supports and complements research conducted by other scientists and previously published by the authors themselves. The authors were also limited by the size of the article itself. The development of the area that was only signaled in the article also requires continuation. This concerns the presented state and transition diagram. The time the system spends in individual states (clusters) can be modeled and used to predict past performance. The authors see here significant support for the operation of the system in dynamic conditions. The variable power generated by RESs and the variable demand for electrolyzer power will be able to be effectively predicted with accuracy to the probability distribution based on archival data. The data presented in the article can be continued with the consideration of other months of the system’s operation. Here we have in mind the winter months, characterized by very high energy production from the wind turbine and very low production from the photovoltaic system.

5. Conclusions

The article analyzes and studies the power generation by the photovoltaic–wind mix in two characteristic months. April was characterized by high energy production from the wind turbine and the average energy production from the photovoltaic system. In May, the system generated average amounts of energy from the wind and large amounts of energy from the photovoltaics. The preliminary research and statistical analyses demonstrate that in both analyzed months, the generated power in the mix is subject to mutual replacement and complementation with the power generated by individual RES. This is particularly visible in the histograms of the density of individual power levels for individual RESs and for their mix. In April, a graph of considerable interest was obtained on the histogram corresponding to anti-fragile properties. Generating power from a photovoltaic–wind mix fits into the concept of an anti-fragile system because it uses complementary energy sources—the wind (often stronger at night and in winter) and the sun (more efficient during the day and in summer), which allows for a better adaptation to changing weather conditions and increases resistance to disruptions. Such a system not only minimizes the risk of energy shortages but also benefits from environmental instability, because distributed production and adaptive control enable optimal use of available resources.

The unsupervised clustering performed using the k-Means algorithm provides significant findings regarding the process of generating power from the RES mix and its use in the low-emission hydrogen production system. In these areas, the following conclusions can be drawn from the conducted research:

• The Silhouette Coefficient research supported by expert validation led to the division of the two-dimensional space of generating power from the photovoltaic system and the wind turbine into 9 clusters.
• The division of the state space into 9 clusters is sufficient for an accurate description of the power generated from the RES mix for the production of low-emission hydrogen. The clusters were numbered and named, and their usefulness for balancing the entire system was demonstrated. The performed clustering became the basis for the operational analysis of the low-emission hydrogen production system from the photovoltaic–wind mix.
• The relative frequency of their occurrence was calculated for individual clusters. It has been demonstrated that such calculations can be used to characterize the quality of the photovoltaic–wind mix in individual months of the year.
• In the analyzed month of April, 25% of the energy generated in the photovoltaic–wind mix came from the photovoltaic system. The low-emission hydrogen generation process was in states (clusters), ensuring that the operation of the electrolyzer with nominal power amounted to 57% of the total operating time in that month. In May, the share of photovoltaics in the generated power was 45%. The low-emission hydrogen generation process was in states, ensuring that the operation of the electrolyzer with nominal power amounted to 43% of the total time in that month. In the remaining states of the hydrogen generation process, the power must be drawn from the energy storage system. The cluster analysis also showed the functioning of the operating states of the power generation process from the mix, which ensures the charging of the energy storage.
• The graphs of the occurrence of power generation states (of individual clusters) in individual hours of the day confirm the complementarity and substitutability of some power sources by others in the mix. The operational analysis performed has shown the usefulness of clustering in balancing the low-emission hydrogen production system from the energy of the photovoltaic–wind mix.
• The most detailed operational analysis of the clustering process was performed using the so-called heat maps. Using this technique of imaging the results obtained in clustering, it is possible to quantitatively describe the power generated by the photovoltaic–wind mix and its use for the production of low-emission hydrogen.
• The operational analysis showed the need to use low-emission hydrogen production from the energy from the RESs mix of energy storage systems in the system. The data from both months presented in the form of heat maps confirmed the need to store excess energy produced in ESS and return it to the process during periods of lower energy production. The latter occurs in the morning and evening periods, which are very well visualized by heat maps. The obtained clustering shows that ESS would be charged and discharged twice a day.

The research and analyses conducted in the article confirmed the presence of favorable climatic and geographical conditions for the production of low-emission hydrogen from the photovoltaic–wind mix in the Lublin region in Poland. This fact, combined with the production of artificial fertilizers, industrial chemicals, and hydrogen buses in this region, creates highly conducive conditions for the climate and energy transformation of the entire region. The authors intend to continue to support local entrepreneurs in this area.

Quantitative research results in the form of record statistics within one cluster and detailed cluster boundaries will be the subject of our future works and scientific articles. Quantitative data related to the presentation of the process in specific states and in specific periods of time can also be used to determine the energy storage. However, this requires advanced data processing within individual clusters on a daily basis.