Probabilistic Analysis of Electricity Production from a Photovoltaic–Wind Energy Mix for Sustainable Transport Needs

Abstract

Renewable Energy Sources (RESs) are characterized by high unevenness, cyclicality, and seasonality of energy production. Due to the trends in the production of electricity itself and the utilization of hydrogen, distributed generation systems are preferred. They can be connected to the energy distribution network or operate without its participation (off-grid). However, in both cases, such distributed energy sources should be balanced in terms of power generation. According to the authors, it is worth combining different RESs to ensure the stability of energy production from such a mix. Within the mix, the sources can complement and replace each other. According to the authors, an effective system for generating energy from RESs should contain at least two different sources and energy storage. The purpose of the analyses and calculations performed is to determine the characteristics of energy generation from a photovoltaic system and a wind turbine with a specific power and geographical location in the Lublin region in Poland. Another important goal is to determine the substitutability of the sources studied. Probabilistic analysis will be used to determine the share of given energy sources in the energy mix and will allow us to estimate the size of the stationary energy storage. The objective of these procedures is to strive for the highest possible share of renewable energy in the total energy required to charge electric vehicle fleets and to produce low-emission hydrogen for transportation. The article proves that the appropriately selected components of the photovoltaic and wind energy mix located in the right place lead to the self-balancing of the local energy network using a small energy storage. The conclusions drawn from the conducted research can be used by RES developers who intend to invest in new sources of power generation to produce low-emission hydrogen. This is in line with the current policy of the European Union aimed at climate and energy transformation of many companies using green hydrogen.

1. Introduction

In recent years, many countries around the world have seen a huge increase in investment in Renewable Energy Sources. They usually take the form of large ground-mounted photovoltaic systems that cover areas of many hectares [1]. The second most popular renewable source is wind energy [2]. In this case, wind turbines are in the form of turbines which are over 200 m high and capable of generating between 3 and 7 MW. Thus, the landscape of a world independent of fossil fuels will increasingly include the energy components for the production and storage of electricity [3], as shown in Figure 1.

Due to the intensive development of science in the field of materials and electrical engineering, photovoltaic systems can generate more and more power from a unit of surface area [4]. In the third decade of the 21st century, bifacial photovoltaic panels capable of generating a peak power of almost 600 Wp from a single panel with a surface area of 2278 mm × 1134 mm are already a standard [5]. Bifacial panels have active layers on both sides, so the generated power is greater than from the traditional single-sided panels [6]. At this point, it is worth mentioning that the innovative photovoltaic materials are based on perovskites [7,8]. Perovskites can be installed not only on the roofs of buildings but also on their facades or balcony railings. The partial transparency of perovskite cells would even allow them to cover windows in office buildings, factories, or public buildings. Today, not only is covering windows with perovskite films being considered, but also the production of windows with cells already embedded in them.

Also, in the field of wind energy, great progress is observed. Until recently, wind turbines with a capacity of 2 MW were the standard [9]. Currently, turbines with a capacity of over 3 MW are being installed, and the project plan already includes the ground turbines with a capacity of up to 7 MW and the marine turbines with a capacity of up to 16 MW [10].

However, the generation of energy from renewable sources is not only about creating huge land and marine farms. There are also millions of small, distributed power generation systems in the form of rooftop photovoltaic systems, ground-mounted systems, and carports [11]. Distributed energy already allows for the production of significant amounts of electricity in many countries and, thus, replaces the electricity produced in combined heat and power plants using coal and natural gas [12]. In April 2024, Poland exceeded 30% of the share of energy from renewable sources in energy production and consumption for the first time in history [13]. Low-emission sources accounted for almost 3/4 of electricity production in the European Union in the first half of 2024. In the entire European Union, solar energy production increased by 21% (+25 TWh) in the first half of 2024 compared to the same period a year earlier. In turn, wind energy production increased by 9% (+20 TWh). In total, the volume of energy from these two renewable energy sources increased by 45 TWh, and their contribution to the generation of electricity within the European Union reached a record-breaking 30%. [14].

The large annual increases in the number of photovoltaic and wind systems connected to the distribution grids cause problems with balancing the power networks [15]. The amounts of energy produced from the photovoltaic and wind systems are dependent on weather conditions [16]. Energy generation from photovoltaic systems is characterized by cyclicality related to the times of day and night and seasonality resulting from the changing seasons [17]. Seasonal variations and unpredictable weather conditions affect the amounts of energy produced by the wind turbines as well [18].

Institutions and people involved in balancing power networks continue to point out the huge problems associated with this task [19]. To balance the supply and demand for renewable energy, network operators must deploy expensive resources to ensure the flexibility of network management [20]. Energy storage technologies such as batteries and hydroelectric storage can facilitate the storage of excess renewable energy during periods of low demand and discharge it when the demand is high [21]. Demand response programs can encourage consumers to shift energy consumption to the times of the day when renewable energy is abundant, reducing the need for expensive peak generation.

Despite countless efforts, Poland often experiences situations where the distribution network operators refuse to connect the new renewable generation capacity (both wind and photovoltaic systems). Furthermore, instances of grid imbalance are also common, i.e., when the voltage in the grid increases and causes renewable sources to cease operation.

In such situations, scientists provide substantive assistance. Many innovative techniques for balancing power networks that work with different renewable energy sources have already been developed [22]. The photovoltaic and wind systems have been thoroughly characterized [23]. Scientists have developed many advanced models that can be applied in the field [24]. In addition, scientific articles from the last few years also include techniques, models, and algorithms for predicting energy generation in the near and distant future. Considerations in the field of balancing energy production and consumption concerned both small individual households, institutional buildings, small and large manufacturing companies, as well as entire cities, islands, and countries. Analyzing the practical examples published in the articles, one can find many good practices that can be implemented in other places in the world. In the literature, one can also find many examples of unsuccessful projects that readers can avoid in their work.

Scientists currently use various methods to predict the amount of energy produced by photovoltaic systems. Acquisition and processing of substantial amounts of data (Big data) is facilitated by the high computing power of current computers and advanced machine learning methods. Scientists make predictions in an ultra-short period of time [25], in a short period of time [26], and mid-term [27] for the energy produced by photovoltaic systems. CFD models are used for spatial extrapolation of the wind field over complex terrain [28]. Scientists also quantify temporal irregularities in the solar wind for the purpose of long-term sequence prediction [29]. Performance predictions are also made for single wind turbines [30], as well as for large wind farms consisting of multiple wind turbines [31]. Advanced modeling techniques of wind turbine performance allow the production of accurate predictions on their performance [32]. Among other things, neural networks are used for this purpose [33,34]. Remarkably interesting are the case studies of energy production from renewable sources in individual countries or regions of the world. The researchers have made interesting analyses in the area of renewable energy status in Azerbaijan [35], prospects and obstacles associated with community solar and wind farms in Jordan [36], investigation of wind power potential in South Africa [37], South Korea [38], Comoros [39], Iran [40] and in many countries of the European Union [41,42]. Due to their place of residence, the authors follow the development of systems in Central and Eastern Europe [43]. The harmful impact of wind turbines on the lives of humans and animals, as well as on the disruption of telecommunications systems, is also being investigated [44].

To meet the expectations of the energy market and the individual producers of electricity from various Renewable Energy Sources, the authors decided to support the processes of balancing the energy networks powered by the energy from large ground-based photovoltaic farms and wind turbines [45]. According to the authors, stationary energy storage devices are necessary for the effective balancing of energy networks with RES generators with a capacity of several MW [46]. The author’s visit to the Intersolar Trade Fair in Munich in 2024 confirmed that numerous technologies are currently available on the market for storing substantial amounts of energy in short periods of time to balance the energy networks. The prices of stationary energy storage devices with large energy capacities are already low enough to consider their use for balancing the energy networks by entities external to the owners of the energy networks and the owners of individual renewable energy sources.

Many studies presented in the latest articles aim to model the photovoltaic and wind systems and generalize the obtained results to the entire population of similar objects. The context of the conducted research is a specific object and a specific process of generating an energy mix from photovoltaics and wind. The authors are interested in maintaining the identity of the object, although its generative characteristics change over time depending on the date and time, not the place and not the technology and the hardware used. The authors wanted to build a knowledge base supporting predictive and abductive management of this specific object/process. The objective of other authors is to build a statistical description of the process of generating energy from a mix that has features of generalization to the entire population of such objects. The approach presented by the authors in the article emphasizes the need for an individual approach to the analysis of component objects (wind turbines and photovoltaic installations) located in a specific place in Poland, in the Lublin region. The possibility of influencing individual components of the energy mix through the appropriate selection of technical parameters and their location (in a selected geographical context) was emphasized. The main objective of the article is to present a computational methodology leading to the assessment of the possibilities of producing low-emission hydrogen in a specific place in the world. This is related to the ongoing climate and energy transformation in Europe. Many companies are already preparing investments related to the production of hydrogen from energy obtained from renewable sources. Hydrogen has been recognized by scientists and decision-making bodies in the European Union as the basic medium for achieving complete climate neutrality in 2050 and meeting the requirements planned for 2030. The ongoing climate and energy transformation requires the construction of new energy production capacities dedicated to the production of low-emission hydrogen. Due to good sunlight and wind conditions, the Lublin region is best suited for hydrogen production in Poland. The article is dedicated to RES developers and other large companies that are interested in the production of low-emission hydrogen for transport purposes. The specific objective of the article and the authors’ scientific activity is to support companies producing buses with hydrogen fuel cells in Lublin. Low-emission city buses require large amounts of hydrogen fuel. On this basis, the power of individual components generating power and producing electricity from individual RES was selected. The topic was also chosen due to the lack of clear information in the available scientific articles and the belief among companies producing and distributing electricity about the possibility of balancing energy generation processes from various RESs. The article proves that the appropriately selected components of the photovoltaic and wind energy mix located in the right place lead to the self-balancing of the local energy network using a small energy storage.

2. Materials and Methods

Calculations of the energy produced can be performed in three scenarios. The first scenario (Figure 2a) includes the calculation of energy constituting the energy mix (EM) consisting of the energy produced by the photovoltaic system (EFV) and the energy produced by the wind turbine (EW) [47]. The first scenario does not consider the characteristics of the reception of the energy produced. In this scenario, it is enough to add together two-time series of the course of the generated power or the energy produced in each period. The second scenario (Figure 2b) already considers the type of receivers used for the energy produced in the energy mix. This receiver will be the water electrolyzer producing hydrogen (HP) [48]. Electric power receivers in the form of electrolyzers operate continuously and require high power supply stability. The literature contains a lot of information on the requirements for the power supply of alkaline electrolyzers [49], SOE, PEM, and AEM. Therefore, this scenario must include the selection of an electrolyzer with appropriate power, which will operate with nominal power or lower than nominal power if the manufacturer allows such a state. The authors know from their own experience, which is also confirmed by the analysis of the literature, that such a system is not able to balance itself. The high variability of the power generated by renewable sources and the high stability of the power supplying the electrolyzers are not necessarily correlated. In this scenario, it is essential to return the excess energy produced to the power grid and draw the energy from it in times of shortage. In such situations, it is worth considering the third scenario (Figure 2c). It introduces an additional energy storage (ES) [50], which will accumulate excess energy produced by the solar-wind mix and return it in times of shortage of energy from RES. The authors’ task is to make the required calculations and analyses regarding the size of the necessary stationary energy storage to ensure the self-balancing [51] of the energy production system and its use for the production of low-emission hydrogen [52].

The basic premise for the research (paradigm) assumes that each studied object/process speaks with process data, and this is collected in the form of a linguistic knowledge base based on the time series deep learning technology. In the knowledge base, we collect something that defines the identity of the process despite its variability over time. Many decades ago, it was referred to as an object signature for the purpose of machine learning to recognize friendly and hostile objects. An example would be a vector knowledge base collecting signatures. The compatibility of the used RES sources was demonstrated in a selected geographical context (a specific installation in a specific location). Substitutability and complementarity of the selected RES sources were demonstrated. The applied approach also considers the characteristics of the energy receivers in the form of electrolyzers operating at specific power levels. Managing the low-emission hydrogen production process requires stability and continuity of power supply. The knowledge base enables the management of a specific process through predictive reasoning algorithms (predictive and diagnostic). They facilitate optimization, predictive maintenance, and scalability of the system. The article first characterizes each source of power generation and energy production from renewable sources separately. Then, an analysis of the mix consisting of two specific sources is conducted. In this case, the obtained signatures confirm the substitutability and complementarity of the selected RES sources. The signatures also indicate specific periods of time when the energy is generated in excess (surplus) and in deficit. It should be emphasized that these two features (surplus or deficit) are the result of the decisions related to the location of facilities/processes, and they directly affect the size of the energy storage.

Initial analyses include a review and assessment of monthly time series of power generated by the photovoltaic system and wind turbine. The monthly period is justified due to the relative stability of climatic conditions and the period of settlements with the producer and distributor of electricity in Poland and many other countries in Europe and the world. A monthly analysis showed that the research must consider the daily cyclicality occurring in the photovoltaic system and the wind turbine system. Finally, the authors perform analyses in the daily period divided into hourly periods, considering the measurement data from the entire month. In this hourly window, the generated power (MW) and the produced energy (MWh) are analyzed. In addition to the advanced statistical analysis, the authors always perform probabilistic analysis. This enables the precise calculation of the generated power and produced energy in accordance with the probability distribution. Finally, balancing of the produced energy was applied, which allowed for determining the size of the energy storage system (ESS). To facilitate tracking of individual steps in the calculation algorithm, the following data flow diagram was prepared (see Figure 3).

3. Results

In this chapter, the authors will characterize two Renewable Energy Sources. The first of them is the photovoltaic systems, which are extremely popular in Poland and all over the world. The second is the wind turbines. In the conducted analyses and calculations, the authors will consider not only the technical parameters but also the method of installing individual power generation components and their location. Not only in the case of wind turbines but also in the case of photovoltaic systems, the geographical and climatic context is particularly important and must be included in the calculations.

3.1. Power Generation Characteristics of Ground-Mounted Photovoltaic Systems

Photovoltaic systems are already a common element of the landscape in many countries in Europe and the world. The constantly increasing cost of electricity for both manufacturing companies and individual users encourages investing in this type of Renewable Energy Source. Photovoltaic systems are installed on the roofs of single-family houses or on the ground near the house. They have a peak power of 3 to 10 kWp, and enough energy to power a residential house, and the entire farm can be produced. Often, the users of photovoltaic systems in Poland also have electric vehicles that are charged from their own power generation source. Photovoltaic systems do not generate power at night. They start generating power with the first rays of the rising sun. The greatest amount of generated power occurs at noon when the sun is at its highest above the horizon. As time passes, the sun lowers and sets completely. The length of the day in different geographical conditions varies, and this significantly affects the performance of the photovoltaic systems. In addition to geographical locations, climatic conditions influence the production of electricity from photovoltaic systems. The seasonality of the overlap of seasons and local climatic conditions related to cloudiness, rain, and snowfall are taken into consideration. Wind has a significant impact on the performance of the photovoltaic systems. In locations characterized by high wind speeds, photovoltaic systems produce more energy because they are better cooled. For this reason, in the considered climatic conditions (Lublin Province in Poland), monthly energy production is the highest in the spring month of May, when the insolation is already sufficiently high, and the average daytime temperatures are still lower than 20 °C. In addition to the highest insolation in Poland, our region is also characterized by particularly good local wind conditions. The photovoltaic systems mounted on the ground and on carports are much better cooled than the systems mounted on the roofs of buildings.

Figure 4 shows the time series of instantaneous power generated by a 3 MWp peak photovoltaic system. The data was obtained from a 3 kWp photovoltaic system and multiplied by 1000. The photovoltaic inverter, being an Internet of Things device, sends a measurement data packet every 15 min, including the currently generated power, calculated energy produced, and diagnostic data [53]. The tested installation was optimized in terms of the azimuth setting exactly to the south and a tilt angle of 30°. A system consisting of 12 monocrystalline photovoltaic panels produced 3203 kWh in 2023. Therefore, the load factor of the photovoltaic system for 2023 can be calculated from the formula: 3203 kWh/365/24 h/3 kWp = 0.122 = 12.2%. The calculations and analyses conducted in the article employed the data from the above-described system from May 2024. The measurement data read every 15 min gave almost 3000 records in the time series within a month.

The authors in a previously published study investigated the correlation between a 3 kWp and a 40 kWp photovoltaic system [54]. In the following article, a very high correlation between the performance of these two photovoltaic systems was demonstrated (r = 0.9803; p = 0.001; r2 = 0.9610.). Such a comparison was possible thanks to the location of these two systems in the same location (50 m apart), in identical conditions of no shading, with the same azimuth exactly to the south and the same tilt angle. Large wind farms with peak power of 1 MWp and more are currently built using inverters with power of 40, 50, 100, and 150 kW. The use of smaller inverter power is more beneficial due to shorter DC electrical cables connecting the strings of photovoltaic panels to the inverter. The second advantage is the shutdown of a smaller part of the photovoltaic farm in the event of damage to one of the inverters and the need to replace or repair it.

With the above measurement data, the authors decided to display them using the commonly available Microsoft Excel 2010 calculation and presentation software. The data from the entire month of May 2024 was displayed on a daily chart, as shown in Figure 5. However, such a presentation only allowed for an approximate determination of sunrise and sunset and the range of instantaneous power generated during the day, along with the maximum power. Such an analysis only confirms the cyclicality of power generation by the photovoltaic systems due to changes in day and night.

Much more information can be obtained by averaging the photovoltaic system power hourly and presenting it on a daily chart, as shown in Figure 6. The calculation algorithm in the Python programming language summed up all measurement data during the selected hourly periods and calculated their average value. In this way, the average hourly values of the photovoltaic system power were obtained during the entire month of May 2024.

The above characteristics of generating electricity from photovoltaic systems simply require the use of a stationary storage facility. Only a few owners of photovoltaic systems in Poland can store surplus energy generated in the power grid for a limited time and retrieve it at any time. The solution to the problem of producing enormous amounts of energy during sunny summer days is to store it for short periods of time. Energy storage facilities should be large enough to collect most of the surplus energy produced during the day and release it in the evening, at night, and the next morning, when the demand for electricity by the residents of the house is high. The situation is different in the case of manufacturing companies. Companies that need large amounts of energy during the day to power production and processing processes already have their own photovoltaic systems. Many of the Polish companies that have not yet invested in cheap energy from photovoltaic systems have not withstood the market competition and have been closed. Storing energy in stationary energy storage facilities is still quite expensive in Europe. However, an increasing number of companies have decided to install additional energy production capacities from photovoltaic systems to store and use on the same day in the evening, at night, and the next morning. Storing energy in stationary energy storage is, therefore, a solution to the problem of cyclicality of energy production related to the cycles of day and night. Unfortunately, this is not a solution to the problem of seasonality of energy production from photovoltaic systems. The small amount of energy produced by photovoltaic systems, especially in winter in Polish geographical and climatic conditions, does not allow for covering the current demand for electricity during the day. The lack of excess energy produced does not allow for charging the energy storage during the day and receiving it at another time. The arguments presented above show that photovoltaic systems, even equipped with energy storage, are not able to ensure the stability of the energy supply produced by the home or company’s own photovoltaic system throughout the year. For this purpose, the photovoltaic system must be supported by another Renewable Energy Source, which will be less dependent on the seasonality of the overlapping seasons. Of course, there are countries that are characterized by smaller seasonal changes in sunlight, and thus, this problem is less harmful in its effects. The greatest problems related to balancing power networks occur in spring and summer. At noon, the greatest energy production from the photovoltaic systems occurs, and it cannot be consumed by the increased energy demand for air conditioning in the rooms. Stationary energy storage devices can contribute significantly to reducing this effect. However, energy storage devices are only just entering the market in our country, and their use is slowly becoming economically justified.

3.2. Power Generation Characteristics of Large-Power Wind Turbines

To determine the potential of a given location for producing wind energy, the following measurement methods can be applied [55]. The first one is to use wind maps, which are offered by various portals related to measuring meteorological conditions. They only allow for an approximate determination of wind speed in selected locations. Very often, measurement data comes from small heights compared to the currently constructed masts of modern wind turbines. Therefore, the best way to confirm the potential location of a wind turbine is to build a measuring tower with the same height as the planned turbine. Measurements from two different wind speed sensors send the data on the instantaneous and averaged values over a period of 10 min to the cloud server. Measurements were taken throughout 2016 in the location where the wind turbine was finally built. The authors used the wind speed measurement data from May 2016 at a height of 140 m for calculations [56]. Then, the power curve of the Vestas V126 wind turbine with a capacity of 3.45 MW was used to calculate the produced power. Almost 4500 measurement points were obtained and are presented in Figure 7 as a time series. Studies have shown that the average wind speed in May at this altitude was 6.4 m/s. The amount of energy produced this month was 749 MWh, and the average monthly power was 981 kW. During the month, the turbine worked for 744 h, and the power utilization factor was 28%.

The calculations for the power generated by the wind turbine were conducted in the same way as for the photovoltaic system. Figure 8 illustrates the daily values of the power generated by the turbine for the entire month of May. The presentation of the data in Microsoft Excel does not allow for the visualization of any trends and relationships between the power generation during the 31 days of the wind turbine’s operation.

Then, by using the calculation tools developed for the Python programming language, the average hourly power generated by the wind turbine was calculated. The graph of average hourly power values clearly depicts the trends in power generation and, thus, energy production by the renewable wind source (see Figure 9).

3.3. Analysis of Power Generation from Photovoltaic and Wind Energy Mix

The average hourly values of the generated power from the photovoltaic and wind systems and their mix are shown in

Table 1. Basic statistics and quantiles for individual renewable energy sources and their combinations.

	Country	Mean	Std	Min	10%	20%	30%	40%	50%	60%	70%	80%	90%	95%	99%	Max
Pfv	24.00	744.34	883.33	0.00	0.00	0.00	0.33	56.14	250.06	532.89	1345.39	1855.05	2116.30	2205.54	2223.86	2226.20
Pwt	24.00	980.73	379.61	359.30	571.45	689.08	749.86	782.98	913.03	1079.86	1181.84	1346.53	1509.01	1640.18	1657.27	1657.89
Combined	24.00	1725.07	751.84	671.69	891.27	1152.57	1309.76	1385.21	1528.20	1657.35	2003.61	2589.65	2885.14	2988.31	3073.38	3094.13

and Figure 10. Photovoltaic systems generate power only during the day, and at night, their production is zero. This is called daily cyclicity. After the night, with sunrise, the photovoltaic system begins to generate power, the maximum of which falls at noon. After the sun passes beyond the highest point on the horizon, the produced power decreases until sunset. Wind turbines are also characterized by high daily variability of the generated power. The maximum for the presented average power from the windfalls is around midnight. Then, the wind turbine power decreases, reaching a minimum around 8:00 A.M. After that, it increases again and maintains a relatively constant value between 10:00 A.M. and 5:00 P.M. In the evening, the wind starts to blow stronger again, which translates into an increase in the produced power until midnight. The sum of these two previously described powers has an interesting course. At night, it is clearly visible that the power from the wind turbine constitutes 100% of the total power produced. During the day, the share of both sources in the mix is different and depends on the time of day, reaching a maximum at noon. The characteristics of total power clearly show two minimums. The first one occurs in the morning when the wind turbine generates less power than at night, and the photovoltaic system has not yet reached high power due to the rising sun. Then, the total power increases with the speed of the increase in the power from the photovoltaic system when the power from the wind turbine is practically constant. The maximum of the combined power occurs around 01:00 P.M. After passing the optimum, the total power also decreases with the decrease in power from the photovoltaic system, reaching a second minimum around 08:00 P.M. After this time, 100% of the generated power derives from the wind source.

The average hourly values of the power generated during the month are presented in Figure 10 as a line graph. The same values are presented in Figure 11 as a bar graph. The linear graph more clearly shows the trends in the change in the power of individual RES. The hourly data presented in hourly intervals in the bar graphs also represent the hourly energy production in kWh.

Multi-day (monthly) average hourly graphs can be used as a location-equipment signature of the studied energy mix (identity). Such signatures can be used for geographic-equipment categorization of potential locations of RES power generation systems.

Now, let us examine the characteristics of the combined power from the photovoltaic and wind mix. The minimum, maximum, and average values of the average hourly power constituting the combination of the energy sources from the photovoltaic system and the wind turbine are presented in Figure 12. From the analysis of these data, peculiar conclusions can be drawn regarding the energy production in this particular energy mix. The authors consider the course of power in periods of 1 h to facilitate the calculation of the energy produced during this time. As a reminder, generating the power of 3000 kW (3 MW) for a period of 1 h results in the production of energy of 3000 kWh (3 MWh). The analysis was started at midnight. From midnight to morning hours (from 00:00 to 5:00), the only component of power generated in the energy mix is the power from the wind turbine. The minimum value in this period is 0. This indicates that there were entire hours during the month in selected hourly intervals without the production of power generated from the wind turbine. The maximum values of the power generated by the turbine were over 3000 kW. At the same time, the average values of the generated power ranged from 1000 to 1500 kW with a decreasing trend from midnight to the morning hours. From 6:00 A.M., the power and energy from the photovoltaic system begin to appear in the energy mix. The component of the mix coming from the solar source means that the minimum values are never equal to 0. The minimum values of the power generated in the mix increase to a value of over 1500 kW at noon. This is the result of the Sun rising and reaching higher and higher altitudes above the horizon. The maximum and average values of the generated power behave similarly to the minimum values of power, except that the maximums for them fall at 01:00 P.M. After that time, the minimum, maximum, and average power values in the mix decrease until 08:00 P.M. (sunset). From 09:00 P.M. till midnight, the power generated in the mix again consists only of the power from wind. Also, in this period, the minimum power is equal to 0. The average maximum power in the mix again reaches values higher than 3000 kW, and the average power significantly exceeds 1000 kW with a growing tendency to a value of almost 2000 kW.

Many scientists prefer to present this type of data as box plots, as shown in Figure 13.

The share of hourly average power from individual energy sources in the energy mix is presented in Figure 14. The considered hourly average power confirms that the wind is a more stable renewable energy source. Throughout the month, there was no occurrence when the hourly average power was equal to 0. The average power generated by the photovoltaic systems begins its 1% share in the mix from 5:00 A.M., reaches a record 75% at noon, and then decreases to 3% at 08:00 P.M. The standardized share of two energy sources in the energy mix is shown in Figure 15.

In the area of qualitative analysis of complementarity between the power generated by the photovoltaic system and the wind turbine, the results presented in Figure 15 should be described in more detail. The data presented there show a measure of the substitutability of the power produced by one source with the power generated by the second energy source. For example, a photovoltaic system that is not operating at night does not generate power and its share in the energy mix is 0. At that time, the share of power generated by the wind turbine is the only source of power and its share in the energy mix is 1. This indicates the complete substitutability of the photovoltaic system with the power from the wind turbine. The situation can also be reversed when there is no wind during a sunny day. Then the photovoltaic system can be the only source of power in the mix and its share will then be equal to 1. However, this did not happen in the data analyzed. Complementarity can be defined as the substitutability and complementarity of one energy source by another. Since in the case under consideration there is stochastic uncertainty and cognitive analysis of power complementarity in the energy mix must be considered with accuracy to the probability distribution (see Table 1). Complementarity of one power source by another occurs when the share coefficient for both sources is less than 1. The analyzed energy mix may have a different share of both power sources depending on the time of day (see Figure 14 and Figure 15).

4. Discussion

In addition to the advanced statistical analysis, the authors always perform the probabilistic analysis [57]. It allows the calculation of the generated power and produced energy with accuracy to the probability distribution.

Figure 16 and

Table 2. Probability of generating individual power levels from a solar-wind mix.

Time	00:00	01:00	02:00	03:00	04:00	05:00	06:00	07:00	08:00	09:00	10:00	11:00	12:00	13:00	14:00	15:00	16:00	17:00	18:00	19:00	20:00	21:00	22:00	23:00
Level_750	0.69	0.61	0.58	0.58	0.61	0.55	0.42	0.29	0.39	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.97	0.94	0.94	0.81	0.68	0.71	0.77	0.77
Level_1000	0.69	0.52	0.52	0.48	0.52	0.35	0.29	0.16	0.16	0.84	1.00	1.00	1.00	1.00	1.00	1.00	0.97	0.94	0.87	0.61	0.58	0.58	0.74	0.77
Level_1250	0.56	0.48	0.42	0.35	0.29	0.26	0.23	0.10	0.10	0.39	1.00	1.00	1.00	1.00	1.00	1.00	0.94	0.81	0.65	0.45	0.48	0.55	0.52	0.68
Level_1500	0.53	0.42	0.42	0.29	0.29	0.19	0.16	0.06	0.10	0.32	0.97	0.94	1.00	1.00	1.00	0.90	0.94	0.68	0.42	0.39	0.45	0.52	0.52	0.61
Level_1775	0.38	0.35	0.32	0.26	0.19	0.19	0.13	0.06	0.06	0.16	0.87	0.90	0.97	0.94	0.97	0.84	0.77	0.45	0.35	0.29	0.29	0.48	0.45	0.48

present the probabilities of achieving the required power generation levels by the RES mix. The calculations were made for the power levels of 750 kW, 1000 kW, 1250 kW, 1500 kW, and 1750 kW. It is clearly visible that the probabilities of achieving lower power levels are higher. The following is a guide to interpreting the calculation results. In the hours from 10:00 A.M. to 3:00 P.M., power levels of 70, 1000, and 1250 kW were achieved with probability 1. This is possible because of the power obtained from both renewable sources. The RES mix is not able to ensure the lowest power generation level of 750 kW with a probability of 1 throughout the day. The problem with the stability of generating individual power levels is the probability of generating power at night, which is lower than 1. In the period from 00:00 A.M. to 8:00 A.M., the generated power at individual levels is characterized by a probability below 0.7. The situation is more favorable for the evening hours. The probability of generating individual power levels in the hours from 07:00 P.M. to 11:00 P.M. is from 0.29 to 0.81. The power generation level of 1750 kW has never been achieved with probability 1 during the day. In the daytime hours, from 10:00 A.M. to 04:00 P.M., the probability of reaching the power level of 1750 kW is from 0.77 to 0.97. The power generated during individual hours of the day is a random variable whose hourly probability distributions in the night, afternoon, and evening hours are close to an exponential distribution.

To determine the size of the energy storage, it is necessary to consider what excess energy (measured in kWh) occurs in individual hourly intervals for individual power levels. Figure 16 illustrates the surplus and the deficit of energy for different power levels at which the electrolyzers operate. It is worth recalling that to ensure a constant power level of 1000 kW during the day, the RES must produce 24,000 kWh of electricity. To ensure continuous power supply to the electrolyzers with a power of 1750 kW during the day, 42,000 kWh of energy is needed. The data presented graphically in Figure 16 are also presented numerically in

Table 3. Energy balance for individual levels of generated power from the solar-wind mix.

Level	Energy Surplus [kWh]	Energy Deficit [kWh]	Balance [kWh]	Energy Surplus (Model) [kWh]	Energy Surplus (Model) [kWh]
Level_1000	18,171.63	−786.57	17,385.06	18,188	−802.7
Level_1250	13,290.06	−1905	11,385.06	13,282	−1896.7
Level_1500	9583.75	−4198.69	5385.06	9626	−4240.7
Level_1750	7199.92	−7814.86	−614.94	7220	−7834.7
Level_1724.38				7409	−7409

.

Lublin has two factories of buses powered by hydrogen fuel cells. It is, therefore, worth comparing the daily energy production from the energy mix to the hydrogen production capacity. The production of one kilogram of hydrogen requires approximately 50 kWh of energy. The energy mix is likely to provide the power to 1000 kW electrolyzers during the day. The energy produced during the day is 24,000 kWh and is enough to produce 480 kg of hydrogen per day. A city bus usually has tanks that can hold up to 40 kg of hydrogen compressed to 350 bar, which gives it a range of over 400 km. The hydrogen produced daily can, therefore, fully refuel 12 buses and provide them with a total range of 4800 km.

Now, let us consider the scenario of a continuous power supply of electrolyzers with a power of 1750 kW. The energy produced during the day, amounting to 48,000 kWh, is sufficient to produce 960 kg of hydrogen per day. Therefore, the daily hydrogen production can fully refuel 24 buses and provide them with a total range of 9600 km. However, the probability of obtaining such a constant power supply of electrolyzers is low outside the afternoon hours. To produce about 1000 kg of hydrogen per day, the investor must consider the use of an energy storage system.

Let us now analyze the data presented in Figure 17. In the hours from 10:00 A.M. to 05:00 P.M., excess energy is generated relative to all assumed power levels. In the hours from 06:00 P.M. to 09:00 A.M., a deficit occurs at the selected power levels. Of course, the greatest deficit occurs for the highest level of power demand, i.e., 1750 kW. Based on the data presented in the figure, there is a need to store the excess energy during the day and return it to the hydrogen generation system in the evening, night, and morning hours [58].

The simplest processing of the data contained in Figure 17 using a Microsoft Excel 2010 tool provides interesting results. Using this tool, the excess and the deficit energy were summed up for individual levels of electrolyzer power. The results of these calculations are presented in Table 3. They demonstrate that the largest excess of energy produced from the mix occurs for the receiver power level of 1000 kW. The excess energy is over 18,000 kWh, with a deficit of almost 800 kWh. This means that even the smallest level of selected electrolyzers cannot be powered only from the RES mix. There is a small energy deficit. These analyses lead to the conclusion related to the smallest size of the stationary energy storage. To ensure hydrogen production using only energy from RES, the deficit cannot occur at all [59]. Therefore, the smallest energy storage needed to ensure the stability of the electrolyzer’s power supply with 1000 kW from RES is a storage with an energy capacity of 1000 kWh (1 MWh). The figures were rounded up due to the adopted simplifications in the calculations and the capacity series of the energy storage devices offered on the market. Powering the electrolyzers with a power of 1000 kW is the least advantageous due to the smallest amount of hydrogen produced and an exceptionally large amount of energy returned to the grid. At this load, the amount of energy used to produce hydrogen would be 24,000 kWh, and the amount of energy returned to the power grid would be over 17,000 kWh. The most balanced in terms of energy production and consumption is the operation of electrolyzers with a power of 1750 kW. The average excess of energy produced during the day is slightly over 7000 kWh, with a slightly larger deficit at the same time. A negative balance of approx. −600 kWh means that this amount of energy would have to be taken from the power grid. In the total energy balance of over 49,000 kWh (42,000 kWh + 7199.92 kWh), this is slightly over 1% (exactly 1.25%). Based on these calculations, it can be concluded that the optimal energy storage should have an energy capacity of 8000 kWh (8 MWh). This would ensure that all the energy produced from the solar-wind mix is used to produce green hydrogen [60]. Using the methodology and the calculation algorithm presented in the article, it is possible to compare different compositions of the energy production sources in the energy mix (the ratio of the power from the photovoltaic system to the power from the wind system) located in one place. This analysis can also be used to predict the performance of systems located in different countries. The authors’ latest research has shown the impact of the location of a photovoltaic carport with the same peak power on the possibilities of producing low-emission hydrogen in Poland and Italy [61]. It also includes a broader discussion of the role of energy storage systems in low-emission hydrogen production systems.

In relation to the universality of the method for determining the capacity of the energy storage, is presented a graph of the dependence of the Energy Balance on the Electrolyzer Power. The purpose of energy balancing is the situation of the complete use of energy produced by the energy mix for the production of low-emission hydrogen.

The intersection of the Energy Balance function with the x-axis at value 0 gives the optimal electrolyzer power (yellow dot on the graph in Figure 18). This means that all the power generated in the energy mix is transferred to the needs of hydrogen production. Solving the regression model equation from Figure 18 gives the optimal electrolyzer power of 1724.38 kW.

The next step is to determine the energy storage capacity for the electrolyzer power of 1724.38 kW. This can be done by creating a regression model of the excess energy in the mix and the deficit energy in this mix (Figure 19). By inserting the optimal value of the electrolyzer power into the regression equations in the form of 2nd degree polynomials, we obtain the optimal energy storage capacity (ESC) of 7409 kWh. The analytical approach used can be easily verified because the value of the excess energy should be equal to the value of the deficit energy for the optimal electrolyzer power. This is presented in the last row of Table 3.

The article shows that integrating various renewable energy sources into effective energy mixes is not easy, but it is possible. Very detailed planning of the entire investment is necessary. It should begin with a thorough analysis of the needs related to the volumes of hydrogen produced. The biggest problems related to balancing energy networks result from the lack of correlation between energy demand and supply. The amount of energy produced can be controlled by selecting the appropriate proportions between energy from photovoltaic systems and wind turbines. The arrangement of photovoltaic panels in the east-west direction influences the amount of energy produced, especially in the morning and afternoon hours. This will reduce the energy deficit from the energy mix in the morning and afternoon hours, which will result in the possibility of using a smaller energy storage. The calculation methodology prepared by the authors, together with the software, will allow its reuse for the analysis of other cases of energy mix compositions. The tools used can also be incorporated into algorithms operating online for the purposes of optimization in energy production processes and its use for generating low-emission hydrogen.

The approach presented in the article to the production of low-emission hydrogen from a carefully planned energy mix consisting of energy from photovoltaic systems and wind turbines has many advantages. The previously used approach with energy from only one renewable source required energy balancing based on the power grid and led to many problems. By building efficient and self-balancing electricity production systems, it is also easier to obtain permission to connect new energy production capacities to the power grid.

The use of V2G (vehicle-to-grid) technology will also allow for the possibility of storing electricity in vehicle traction batteries and releasing it during periods of deficit. This approach makes sense and is economically justified, especially with the continuous increase in the number of electric vehicles and the increasing energy capacities of batteries. The authors intend to follow the latest global trends in these areas and conduct research supporting them.

5. Conclusions

The authors of the article presented the characteristics of power generation and energy production from the most popular Renewable Energy Sources in Poland. These include the photovoltaic systems and the wind turbines. The impact of different geographical and climatic conditions on their performance was determined. The characteristics of both sources affect the unpredictability of the performance of these systems, which creates problems with balancing the power grids to which they were connected. In relation to the photovoltaic systems themselves, the solution to the problem of cyclical production from the Sun is stationary energy storage, which allows the use of the energy produced during the day and throughout the day. However, energy storage is a helpful solution for short-term energy storage, up to a few days at most. Energy storage does not solve the problem of the seasonality of energy produced from the Sun. The amount of daily and monthly energy produced during the winter months is much lower than in the spring and summer periods. Therefore, the authors analyzed the generation of power and energy production from two Renewable Energy Sources in the form of photovoltaic systems and wind turbines. The analysis covered the generation of power by the photovoltaic system with a peak power of 3 MWp and the wind turbine with a power of 3.45 MW. The analyses and calculations performed in May allowed us to determine the possibilities of replacing and supplementing the generated power by these two sources. The research showed that the power generated by wind turbines largely replaces photovoltaic systems that are inactive at night. The research also showed very interesting possibilities for supplementing these two sources in the morning and afternoon periods. Advanced probabilistic analysis also allowed to determine the size of the energy storage, which was considered by the authors to be an essential element of the entire ecosystem of generating the power from the renewable sources. Determining the minimum, effective size of the energy storage is particularly important due to the excessive cost of this type of device. This cost largely affects the total cost of return on investment. This applies to those engaged in the development and investment in new renewable energy capacity intended to generate electricity for charging large fleets of electric and hydrogen vehicles (e.g., buses).

Advanced statistical analysis and probabilistic analysis allowed us to estimate the minimum and maximum size of the stationary energy storage. From the mix of the energy from the photovoltaic systems with a peak power of 3 MWp and the wind turbine with a capacity of 3.45 MW, monthly energy production of over 49 MWh is possible. Calculations were made for one sample month of May, considering the geographical context related to the location of both systems in the Lublin Voivodeship in Poland. The conducted research and analyses allowed for the formulation of the following specific conclusions:

• Energy from the tested energy mix is not able to ensure the stability of the power supply of hydrogen electrolyzers operating with a power of 1000 kW. For this purpose, it is necessary to draw energy from the power grid or use an energy storage with an energy capacity of 1000 kWh. The energy produced from the energy mix to power the electrolyzers will then amount to 25,000 kWh and will be enough to produce 500 kg of hydrogen per day. This results from the need to supply 50 kW of energy to produce 1 kg of hydrogen. This amount of hydrogen will be enough to fully refuel a fleet of more than 12 hydrogen buses, each of which will have a range of over 400 km;
• The use of the entire amount of energy produced in the mix is possible in the case of selecting electrolyzers with a capacity of 1724.38 kW and energy storage with an energy capacity of 7409 kWh. The entire daily energy production of 50,000 kWh will then be used to produce 1000 kg of hydrogen by day. This amount of hydrogen will be enough to fully refuel a fleet of 25 hydrogen buses, each of which will have a range of over 400 km;
• The most economically viable option is to power the electrolyzers with a power of 1750 kW from the photovoltaic and wind mix. Operating the electrolyzers with lower power will result in lower daily hydrogen production. In addition, the energy that is overproduced will have to be supplied to the power grid, usually at a very unfavorable price.

Based on the conducted research, general conclusions can also be drawn:

• The Lublin Province in Poland has good geographical and climatic conditions to produce electricity from the photovoltaic systems and the wind turbines;
• Due to the instability of energy production by individual RES, it is impossible to use only one renewable source to power low-emission hydrogen production systems, which require constant power supply and continuous operation;
• To power low-emission hydrogen production systems, it is necessary to use at least two RES together with energy storage;
• Within the solar-wind energy mix, the generated power and energy produced by individual RES replace and complement each other. This has a significant impact on the stability of energy generation by various RES and facilitates the balancing of the power grid;
• It is possible to influence the total generated power and the amount of energy produced in the energy mix by selecting the proportions of individual RES power;
• The total generated power and the amount of energy produced in the energy mix can be realistically influenced by the precise geographic location of the wind turbine and the photovoltaic system;
• The use of small energy storage units in relation to the amount of energy produced daily from the solar-wind energy mix feeding hydrogen electrolyzers can achieve a self-balancing system.

The conclusions drawn from the conducted research can be used by RES developers who intend to invest in new sources of power generation to produce low-emission hydrogen. This is in line with the current policy of the European Union aimed at climate and energy transformation of many companies using green hydrogen. The authors intend to continue the research they have started. The next stage will be a detailed statistical and probabilistic analysis performed for the energy produced from two different RESs throughout the year.