Evaluation of the Possibility of Using a Home Wind Installation as Part of the Operation of Hybrid Systems—A Selected Case Study of Investment Profitability Analysis

Abstract

The renewable energy sector is becoming key to the energy transformation processes of modern economies. The energy policy of one of the European countries specifies that by 2030, about 7% of energy production will come from wind sources. Because wind turbines are becoming more and more efficient, innovative projects are being created to expand their potential by integrating them with the energy systems of existing residential buildings. The analysis of the profitability of such investments may be important for the implementation of such an ambitious plan. In particular, this argument may be crucial for the growth of the potential and development prospects of distributed energy systems based on renewable energy sources. The article outlines the challenges related to forecasting generation from this energy source. The article aims to present the methodology, energy potential and forecasting results of energy generation from wind sources for two selected locations in one of the European Union countries, Poland. The NPV-Net Present Value and IRR-Internal Rate of Return methods were used for the study. These methods allowed the authors to calculate the market value of the investment with the assumed boundary criteria and determine the economic efficiency of the investment. The research was carried out in the period December 2023–November 2024 on test wind installations in households. In addition, the article indicates the challenges related to the variability of atmospheric factors and the self-consumption of the wind turbine, which is often difficult to predict due to the lack of turbine efficiency analysis. The presented models showed that the project in their implementation is fully economically justified and will allow investors to make a rational investment decision. These models can be effectively used in other countries and can also be a starting point for discussions on the direction of the development of energy systems based on renewable energy sources.

1. Introduction

Observations of market reality indicate that wind energy is one of the oldest sources of energy. The wind potential was used to drive windmills for various purposes. With technological progress and promoting solutions based on the idea of renewable energy sources, the scope of their capabilities expanded, and windmills began to be treated as power plants generating electricity. Researchers emphasize that the global energy potential of wind is enormous and is estimated to be equal to the current global demand for electricity [1]. However, the development of energy from this energy source is not always dynamic. For example, the main barriers to the development of wind energy in Poland are: limited availability of land for the development of wind farms, especially in places with favorable wind conditions, high investment costs, and quite long waiting times for the delivery of equipment. Polish construction is energy-intensive, technically not adapted to rising energy prices, expensive to operate, often threatening the health of residents and not adapted to the modern standard of living [2,3]. Energy consumption in construction can be significantly reduced by thermal modernization treatments and the use of modern technologies in construction. Another response to the above-mentioned demands may be modern hybrid technologies combining selected renewable energy sources. Considering that small wind farms are increasingly used as an additional source of energy supporting the energy system of a single-family house. This source can be used to heat water in the central heating system or electricity can be fed directly into the power grid [4,5]. Wind farms, apart from using inexhaustible, renewable energy, are ecologically clean energy because they have the advantage of not emitting harmful substances into the environment. However, it must be remembered that they produce energy only when the wind blows at the appropriate speed. Wind turbines use the power of the wind in the range of its speed from 4 to 25 m/s. At wind speeds of less than 4 m/s, the wind power is small, and at speeds above 25 m/s, the turbine is stopped for safety reasons. Apart from the above-mentioned determinant, a more important problem for the future user seems to be the assessment of the economic efficiency of the possible implementation of such an undertaking. This parameter is particularly important for the demand side when an energy advisor signs a contract.

The purpose of the article is to assess the energy potential and economic efficiency of a home wind installation using the example of a selected geographic destination in one of the countries of the European Union, Poland. The choice of destination was not accidental and was dictated by the fact that the Polish wind energy market is one of the most dynamically developing markets in the entire European Union. To assess the achievement of the goal, the legal regulations in force in Poland, the technical and technological parameters of the analyzed devices and climatic conditions were taken into account. The article presents an analysis of the use of a wind turbine for general home applications—a selected case study. The research highlights the economic efficiency of a feed-in tariff in investing in these types of renewable energy sources and highlights the need to improve policy responses to increase their investment attractiveness. Considering that one of the frequently raised key postulates for the further development of distributed energy is the maximum use of locally available energy resources such as wind power.

A novelty of this article is the ability to determine the impact of various environmental factors on the turbine, observing its work at different times of the day and different periods of the year in changing weather conditions. The obtained results provide comprehensive information on the potential benefits resulting from the use of renewable energy sources in Polish climatic conditions and present restrictions related to their implementation. The empirical research approach allowed the authors to calculate its actual productivity based on the actual data from the wind installation. Research was carried out for each day of the month of the analyzed year. The average monthly electricity production at that time was 446 kWh. The obtained data were highly correlated with individual assembly conditions, which are often omitted in the literature. Obtaining this data allowed the authors to indicate the directions of improvements that may contribute to obtaining a more reliable assessment of the profitability of the surveyed installations. The content of the article gives a fresh and innovative perspective and provides essential knowledge for a potential demand side considering investing in this renewable energy source. To our knowledge, this is the first approach to this topic that includes such a comprehensive analysis of wind turbine productivity based on real data, including economic calculation. Responding to the needs reported by a group of energy advisors. The presented research, therefore, fills a gap in the literature on the subject, thus encouraging discussion and further research on this topic.

The structure of the article is as follows. Section 2 reviews the world and national literature on the use of home wind turbines. Section 3 describes the research methodology used to analyze profitability using net present value and payback period calculations. Section 4 describes and discusses the results. Section 5 presents conclusions and perspectives for future research.

2. Literature Review of the Problem

Contemporary researchers emphasize that wind energy is a strategic direction of energy transformation, strengthening energy security and providing an impulse for economic development. The development of wind energy is supported by the global policy (EU policy until 2050-Green Deal) of limiting the use of fossil fuels to produce electricity in favor of renewable sources. According to data from the World Wind Energy Association, the number of newly installed turbines and wind turbine farms is constantly growing. This trend will be particularly noticeable in Central European countries such as Poland. The share of electricity from renewable energy sources in total consumption in Poland until 2022 was relatively small, but an upward trend is visible [6,7]. A large part of Poland has good wind conditions for installing wind turbines, especially small wind turbines. There is an economic niche for small wind turbines that could be installed on private lands to provide energy to individual farms and homes.

Wind turbines enable the conversion of wind kinetic energy into alternating current electricity. Wind energy has been used by humanity since the beginning of civilization. The first installation generating electricity was built in the mid-20th century [8,9,10]. A wind turbine consists of a rotor with blades that converts the energy of the movement of air masses into the energy of rotation of the wind turbine shaft, a gearbox and a synchronous induction machine that converts the energy of rotation into alternating current electricity. Home wind turbines have been a frequent subject of research over the last twenty years, especially in terms of their use as a generator operating at variable speeds. Initial work focused on the properties of turbines with various rotor power methods [11,12,13,14]. The greatest adjustment possibilities and, at the same time, the best dynamic properties are obtained when the rotor is supplied with slip frequency current. It is implemented in vector control systems, to which many works in the field of drive automation have been devoted [15,16,17,18,19,20]. Works devoted to the dynamics of turbines operating as a generator of a wind power plant focus mainly on the dynamic states originating from the wind turbine. The analyzed cases include the impact on the operation of the power plant of sudden gusts of wind and torque ripple on the turbine shaft, caused by the turbine blade being obscured by the power plant beam [12]. Most works in Polish and world literature are devoted to the cooperation of wind farms with the power system and the impact of wind farms on energy quality [21,22,23,24,25,26]. Relatively little information can be found on the impact of network disturbances on the operation of a wind farm. Works devoted to this topic mainly analyze the impact of the power supply network on the generator control system and the operation of the rotor converter in emergency states [27,28,29,30]. However, there are many studies regarding the impact of network disturbances on the mechanical system of the power plant, in particular on the mechanical transmission, which is the weak point of wind farms [31,32,33,34,35]. During the operation of wind turbines, noise is generated, which hurts the environment [36]. Sounds recorded around wind turbines are in a wide frequency range from 0.1 Hz to 16,000 Hz [37,38,39,40]. Therefore, we are dealing with infrasound (0.1–20 Hz), low-frequency noise (up to 200 Hz) and acoustic noise (up to 16,000 Hz) [41,42,43]. The authors note in their works [44,45] that when designing a wind farm, it should be located at such a distance from acoustically protected areas (places of residence) that no sound levels are causing acoustic discomfort. The acoustic power of wind turbines depends on the wind speed. When designing wind turbines, the authors of the works [46,47,48] note that the wind speed increases with the height above ground level [49,50]. However, this does not always happen. The degree of wind speed increase depends on many factors, such as terrain, changes in temperature and atmospheric pressure, and relative air humidity [51]. Noise emissions associated with the interaction of air and wind turbine blades are one of several individual sources of this device [52]. In addition, there is mechanical noise related to the operation of devices installed inside the gondola [53]. In the case of wind turbines, the dominant source is aerodynamic noise associated with emissions dependent on the design of the rotor blade. There may be rapid pressure changes as the blade moves near the turbine support tower [54]. An important factor influencing the value of the measured noise emitted by a wind turbine at a specific measurement point is the acoustic background [55]. As the wind speed increases, the acoustic background level at the height of the measurement points increases [56]. The specificity of acoustic and non-acoustic phenomena occurring during the operation of a wind power plant has been described in many publications. Because wind speed increases with height above ground level, wind farm owners strive to build facilities high enough to optimize their productivity. Currently, advanced wind speed measurement techniques and wind forecasting methods are available. In areas with less wind, i.e., when the average annual wind speed is below 7 m/s, wind turbines are built on towers exceeding 100 m in height. Due to the technological possibilities of constructing a tower with a tubular structure, until recently steel towers were built, less often reinforced concrete ones with a height not exceeding 120 m. Currently, hybrid technology is being used more and more often. It involves making the lower part of the tower in the form of a reinforced concrete pipe, and the upper parts in the form of a steel pipe. There is also an alternative solution, used occasionally, which involves constructing the tower structure as a spatial truss. There are known truss towers of wind turbines with a height of up to 160 m above ground level [57]. From the point of view of the impact of a wind turbine on the acoustic environment, they are poorly attenuated by the air and spread wide distances. Many researchers describe in their publications the presence of infrasonic noise in the vicinity of wind turbines and roads. There are known cases of masking the audible noise of wind turbines on roads with significant traffic. The foundation of home wind turbines is regulated in Poland by a law under which the release from the obligation to obtain a building permit has turbines up to 50 kW and a height greater than 3 m and less than 12 m. However, the location of the windmill on the plot is possible at a distance from the border not less than the total height of the windmill. For the wind turbine to produce more electricity, it should be installed at least at an altitude of 10 m. Then the turbine reaches the best operational parameters, and the generated noise at 35 dB is permissible within the limits of applicable standards. For comparison, the average level of noise in the household is about 40 dB, the whisper is registered at around 30 dB, and a typical vacuum cleaner works with a deafening level of 75 dB [58].

In conclusion, based on the literature review, it can be said that no author has studied the profitability of investing in a backyard wind turbine. Therefore, this work discusses for the first time the economic, technical and regulatory aspects of a domestic wind turbine. In assessing the profitability of the investment, climatic conditions, technical specifications, social, legal and political aspects were taken into account, which is a novel approach to the analysis of this problem. The results obtained will allow the investor to make a rational decision on the possibility of investing in the analyzed sources of renewable energy. The research presented its practical dimension.

3. Materials and Methods

3.1. Characteristics of a Wind Turbine with a Rated Power of up to 2 kW

For the analysis, the authors selected the installation of one of the most popular suppliers in the European market. The Falcon Silence 2 kW (FNSW-2 kW) wind turbine is a modern technological solution designed for the effective use of wind energy in home conditions and small commercial installations. Thanks to its compact size and advanced design, it is distinguished by high efficiency and quiet operation. Technical and functional features of this turbine.

Table 1. Technical specifications of the Falcon Silence 2 kW turbine [59].

Turbine Technical Specifications	Value
propeller diameter, (m)	3.2
rated power, (W)	2000
maximum power, (W)	3060
operating voltage AC, (V)	230
average annual production (with wind 5 m/s), (kWh)	3832
minimum and maximum wind speed, (m/s)	2.5–40
noise level, (dBA)	30
work in the temperature range (at a distance of 50 m with a wind of 8 m/s), (°C)	−40 to +60
turbine weight, (kg)	68

presents its technical specification.

Falcon Silence 2 kW is distinguished by the simplicity of assembly and minimum maintenance requirements. Solid materials used for production and resistance to weather conditions guarantee the long life of the device. Thanks to the compact dimensions, the turbine can be installed on various types of masts and is compatible with popular energy storage systems. Considering the high variability and unpredictability of wind energy production, it is obvious that a certain form of storage for this type of installation is required. Thanks to this, you can use electricity, even if the weather conditions are not conducive to its production, e.g., at night or during cloudy days. Own Energy magazine gives greater independence from supply from the power network, increases autoconsumption and allows savings on electricity bills.

The assessment of the energy potential of the selected wind farm installation site is a key stage in the investment process, which directly affects the efficiency of the wind turbine and the profitability of the entire project. Before deciding to purchase a wind farm, the most important factor to consider is the average annual wind speed in a given region (Figure 1). In southern Poland, where wind speed rarely exceeds 2.5 m/s, investments in wind turbines may not be profitable. Therefore, before deciding on the location of a wind farm, it is worth using individual long-term wind measurements, because atlases and wind maps of Poland, although helpful, do not reflect the full specificity of local conditions. Measuring wind speed allows for a better assessment of whether a given area has sufficient energy potential.

3.2. Estimation of Energy Production Based on Available Meteorological Data

When analyzing the location of a wind farm installation, it is necessary to take into account meteorological data characteristic of this area.

Table 2. Meteorological data from Łeba.

Date	Minimum Temperature (°C)	Temperature Max (°C)	Maximum Temperature (°C)	Wind Speed Min (km/h)	Maximum Wind Speed (km/h)	Average Wind Speed (km/h)	Precipitation (mm)
01.12.2023	−4.2	2.7	−0.2	2.5	27.4	13	2.2
02.12.2023	−0.3	1.5	0.4	2.5	14.4	6	2.3
…	…	…	…	…	…	…	…
27.11.2024	2.9	5.7	4.8	4	23	17.1	0
28.11.2024	4.7	7.3	6	6.1	29.9	17.9	4.4
29.11.2024	4.5	7.4	5.7	8.6	25.9	15.2	4.8
30.11.2024	2.5	5.4	4	13.3	26.3	20	4.8

Source: own study.

presents meteorological data obtained from the Institute of Meteorology and Water Management (IMGW) for the Pomeranian Voivodeship, with particular emphasis on the town of Łeba from December 2023 to November 2024 inclusive.

The power generated by the wind turbine, where individual parameters affect its efficiency, was calculated based on Formula (1).

$$P=0.5 \times \rho \times A \times v^3\times \eta$$

(1)

where:

• P—output power, (W),
• ρ—air density (approximately 1.225 kg/m³ at sea level),
• A—surface swept by the blades,
• v—wind speed, (m/s),
• η—turbine efficiency (usually around 30–45%).

Small turbines are generally mounted at heights up to 12 m, where the wind speed is lower. In a place with good wind conditions for calculating the power of a small turbine, the rated wind speed VN = 6 m/s can be adopted. Then the power will be about 50 W from each m² of high-efficiency turbine surface. For example, a Świderków turbine with a height of 1.2 m and a diameter of 0.5 m, at a speed of 12 m/s has a power of 0.6 kW. Such power is contained in a whole stream of wind with a cross-section. If the turbine receives 40% of its energy from the wind, its power will be 240 W. And in addition, such turbines are usually mounted on the roof of the building, where the wind speed is generally much lower. If the rated wind speed is adopted, the rated power will drop to 30 W. The theoretical turbine performance producers give a maximum of 45%; for calculation, its value of 40% was adopted due to the climatic conditions in a given area.

3.3. Investment and Operating Costs

A turbine with a rated power of 2 kW was adopted for the investment cost analysis. The detailed specifications of the turbine are shown in

Table 3. Investment costs [61].

Element	Cost
Wind turbine FALCON SILENCE 2 kW FNSW-2 kW, (EUR)	2516
Inverter FALCON FNI20/48, (EUR)	645
Controller with built-in resistor FALCON FNW20/48, (EUR)	1140
Installation, (EUR)	182
Price of energy storage, (EUR)	5058

.

The BMZ HYPERION energy storage system was used for research. It is a high-voltage lithium-ion system with a capacity of 7.5–15 kWh, scalable thanks to its modular design (3–6 modules, each with a capacity of 2.5 kWh). It enables cooperation with hybrid photovoltaic inverters, providing emergency power supply in a three-phase system. The system is compatible with inverters from brands such as GoodWe, Sungrow, SMA, Kostal and Fronius. HYPERION is characterized by modularity, security and flexibility, allowing for expansion and adaptation to the user’s needs.

Table 4. Technical data of the 7.5 kWh energy storage [59].

Element	Value
Number of modules	3
Power (nominal/real), (kWh)	9.7/7.5
Nominal voltage, (V)	155
Final voltage (charging/discharging), (V)	175/170
Capacity (nominal), (Ah)	62.7
Maximum charge/discharge current (3 s), (A)	29/40
Maximum discharge power (3 s)/discharge, (kW)	6.2/4.6
Weight, (kg)	107
Operating temperature during discharging, (°C)	−15 to 55
Operating temperature when loading/storing the warehouse, (°C)	0–45/−20–60
Cell chemistry	Li-Ion NMC
Discharge depth (depending on nominal capacity), %	80
Number of complete cycles (with capacity remaining at 60% or 80%)	5000 or 3000
Guarantee	10 year

presents the detailed technical specifications of the energy storage facility.

The operating range in a wide temperature range makes the system suitable for various environmental conditions, and the nominal power of 7.5 kWh combined with the possibility of momentary discharge with a power of 4.6 kW makes the device functional both in home applications and in smaller industrial installations. The research took into account available government funding for “My Wind Power Plant”. This subsidy provides a refund of up to 50% of eligible costs incurred for the investment. The installed electrical power of the wind turbine can range from 1–20 kW, with the program assuming a subsidy of no more than EUR 1.178/1 kW. The subsidy is granted to energy storage with a minimum capacity of 2 kWh and will amount to no more than EUR 1.412/1 kWh. Under the “My Wind Power Plant” program, the height of the small wind turbine structure cannot exceed 30 m. The micro-installation can be located on a plot of land with a building or on the building itself. Small wind energy is the most advantageous form of energy production from renewable sources—it does not produce waste and does not create problems with use, in the cylindrical version it can be placed on the roofs of all buildings, which then act as pillars. Due to Poland’s transition through energy transformation, RES programs are constantly being introduced and modified for prosumers. Maximum financial support under the program covers two main categories: micro wind farm installation and energy storage. The detailed rules are as follows:

• Wind installation:
  • co-financing of up to 50% of eligible costs;
  • the maximum rate is EUR 1150 for each 1 kW of rated powe;
  • for installations with a capacity of 2 kW, the maximum amount of support is EUR 2300.
• Energy storage:
  • co-financing of up to 50% of eligible costs;
  • the maximum rate is EUR 1380 for each 1 kWh of storage capacity;
  • for a warehouse with a capacity of 7.5 kWh, the maximum support is EUR 3910 (despite the higher theoretical rate resulting from the capacity).

As a result, an individual investor can obtain total funding of up to EUR 6210, provided that the technical and formal requirements specified in the program documentation are met.

Like cell phone batteries, wind turbine batteries naturally degrade and their capacity decreases over time and with use. Warranties for energy storage devices are usually measured by a parameter called energy efficiency and a period and guarantee the ability to maintain a specified charge level during the warranty period. Most manufacturers of energy storage devices provide a warranty for the total amount of stored energy for some time, 10 years. Additionally, it is worth paying attention to how much capacity loss is allowed under the warranty. It can be as much as 60% or almost half. Furthermore, the loss of capacity is generally not a linear process, so in the initial period it may be more intense, and later the rate of capacity loss may decrease. This is all within the warranty. Home energy storage devices differ in price, but they also differ in parameters. Two batteries with the same capacity may have the same price, but different amounts of energy covered by the warranty. The battery life discussed here refers to the number of megawatt-hours or kilowatt-hours that can be stored under the battery warranty. The price of the storage depends on the capacity of the energy storage, measured in kilowatt-hours (kWh)—the more energy that can be stored in the battery, the higher the price. Wind turbines, thanks to their longevity and efficiency, are becoming an increasingly popular choice among renewable energy sources. It is estimated that the operating time of such a turbine is about 25 years or even longer, and even after many years of use, the device can maintain an efficiency of 90%. A key aspect of maintaining high efficiency is regular servicing.

3.4. The Economic Dimension of the Analysis of Investments in a Wind System

The economic dimension of the analysis of an investment in a wind system includes the assessment of the profitability and financial efficiency of such a project. The key aspects of this analysis are: Net present value (NPV) and internal rate of return (IRR). Conducting a comprehensive economic analysis of an investment in a wind system is crucial to making informed investment decisions. This type of analysis allows for minimizing financial risk and maximizing potential profits, which is important from the perspective of both private and public investors [62,63,64,65].

The NPV method is a key tool in assessing the profitability of investment projects. It involves comparing the present value of the future cash flows generated by the project with the initial investment outlay. NPV is calculated as the sum of discounted future cash flows less the value of the initial investment. If the NPV is positive, it means that the project generates value over the cost of capital, suggesting its profitability. A negative NPV indicates that the investment is unprofitable because the expected income does not compensate for the expenditure incurred. The NPV method takes into account the time value of money, which makes it more precise compared to simpler investment evaluation methods. The use of the NPV method in the analysis of investment projects is a basic method used to evaluate financial decision-making. This method is widely used in practice due to its ability to take into account both the time value of money and the risk associated with future cash flows. To calculate NPV you need to [66]:

• Estimate the future cash flows associated with the project.
• Select an appropriate discount rate that reflects the cost of capital and risk of the project.
• Discount future cash flows to present value.
• Sum the discounted cash flows.
• Subtract the initial investment outlay from the sum of the discounted flows to obtain the NPV.

$$NPV={\sum }_{t=0}^n{NCF}_{t } \times {CO}_t$$

(2)

where:

• NPV—net present value,
• NCF_t—net financial flows in subsequent calculation periods,
• CO_t—discount factor,
• t = 0, 1, 2, 3, …, n—subsequent years of the calculation period.

The NPV value can also be calculated using the formula [66]:

$$NPV={\sum }_{t=0}^n{\displaystyle \frac{{CF}_t}{{(1+r)}^t}}-l_0$$

(3)

where:

• CF_t—cash flows in period t,
• r—discount rate,
• n—number of periods,
• l₀—initial outlays.

Typically, t = 0 refers to the initial investment outlay, which is presented as a negative value. The NPV method is valued for its objectivity and precision, but its effectiveness depends on the accuracy of forecast cash flows and the appropriate selection of the discount rate. Therefore, it is crucial to carefully prepare analyses and make realistic assumptions about the future.

The IRR (Internal Rate of Return) method is a dynamic method for assessing the effectiveness of investment projects that takes into account the time value of money. IRR is defined as the discount rate at which the sum of the discounted future net cash flows from an investment is zero. In other words, it is the rate of return at which the present value of the investment’s cash inflows is equal to the initial outlays incurred [66].

$$IRR=i_1+{\displaystyle \frac{{NPV}_1 }{N{PV}_1-{NPV}_2}}\times (i_2-i_1)$$

(4)

where:

• IRR—internal rate of return,
• i₁—the value of the interest rate, where NPV > 0,
• i₂—the value of the interest rate where NPV < 0,
• ${NPV}_1$—NPV value calculated according to $i_1$,
• ${NPV}_2$—NPV value calculated according to $i_2$.

In this method, the most important thing is the difference between i₁ and i₂, which should be more than 1%. IRR is a useful indicator when making investment decisions. If the IRR exceeds the cost of capital or the required rate of return, the investment is considered profitable. However, this method has some limitations, especially for projects with irregular cash flows where there may be more than one IRR value, which complicates the interpretation of the results. In practice, due to the complexity of the calculations, IRR is often determined using spreadsheets such as Microsoft Excel, which offers an IRR function to automatically calculate this indicator based on entered cash flows.

4. Results and Discussion

4.1. Electricity Calculations Based on Meteorological Data

Based on Formula (1), calculations were made taking into account a constant value of 0.5, air density of 1.225 kg/m³ (for conditions at sea level) and the area swept by the turbine blades of 8.0384 m². The manufacturer was assumed based on the technical specification of the wind turbine capacity to be 40%. Calculations for each day were performed by substituting these values into Formula (1), and the detailed results are presented in

Table 5. Calculated electricity based on meteorological data.

Date	Average Wind Speed (km/h)	Average Wind Speed (m/s)	P-Electricity Produced (W)	Electricity Produced (kWh)
01.12.2023	13	3.62	92.76	2.23
02.12.2023	6	1.67	45.27	1.09
…	…	…	…	…
27.11.2024	17.1	4.76	211.12	5.07
28.11.2024	17.9	4.98	242.15	5.81
29.11.2024	15.2	4.23	148.27	3.56
30.11.2024	20	5.56	337.77	8.11

Source: own study.

, which contains all key parameters and calculations for the analyzed period.

Table 5 presents data on the operation of the wind turbine, calculated according to Formula (1), taking into account operational limitations resulting from the wind speed range of 2.5–40 m/s and a constant efficiency of 40%. The turbine remains inactive at wind speeds below 2.5 m/s and above 40 m/s, which is reflected in days with zero energy production. Electricity production increases as wind speed increases, reaching maximum values on days when wind speed approaches the upper limit of the turbine operating range. However, production never reaches the level corresponding to the maximum allowable wind speed. The relationship between wind speed and generated energy is non-linear, indicating that small increases in speed in higher ranges can result in significant increases in energy production. The wind installation was connected to the power grid on 1 December 2023. Figure 2 shows an example of the daily production of electricity in selected months.

For example, Figure 3 shows the daily electricity production in November 2024, which amounted to a total of 581.40 kWh. The highest value was recorded on 1 November, reaching a level of approximately 120 kWh, which indicates exceptionally favorable wind conditions at the beginning of the month. After this date, there was a marked decline in production, with a period of minimal energy generation between 5 and 10 November. The second half of the month saw a gradual increase in activity, with several days reaching levels above 40 kWh, particularly around 16 and 21 November. November was characterized by high production variability, with a dominant peak at the beginning of the month and moderate values in the second half.

4.2. Comparison of the Costs of Energy from a Wind Installation with the Costs of Energy from the Grid

The analyzed household has a moderate annual electricity consumption of 2500 kWh. The investor decided to invest in a wind installation integrated with an energy storage facility to increase energy independence and reduce the costs associated with purchasing electricity from the grid. Auto consumption in this case is 40%, which means that a significant part of the energy generated by the installation is used by the investor for his own needs. The wind installation has been designed to best suit the needs of the farm. The investment was possible thanks to high funding for EUR 6207 which significantly reduced the investor’s own cost to EUR 3361. It is worth emphasizing that the total cost of the installation with the energy storage was EUR 9568. Therefore, the investment became more profitable thanks to financial support. The annual electricity yield from the installation in the first year of operation was estimated at 4102.03 kWh. To secure the functioning of the system, the investor took into account service costs of EUR 230 per year and insurance costs of EUR 49 per year. The projected operational life of the installation is 25 years, with an assumed wear factor of 5% per year and inflation of 5%. Thanks to the energy produced, the investor saves on the costs of purchasing electricity, the price of which is EUR 0.34/kWh. The price of electricity was determined based on the average value of prices applicable in Poland in the first year of operation of the investment. Surplus energy sold to the grid at a rate of EUR 0.18/kWh also constitutes an additional source of income. The unit surplus price was calculated based on price data collected from various power plants, using the arithmetic mean method to average the values. Taking into account a discount factor of 4%, the investment was analyzed in detail in terms of profitability long term. For the analysis of the profitability of wind turbines, the discount rate value of 4% was adopted, because it is an investment with a relatively low risk. Costs related to the energy independence of a household, taking into account operation and statistical assumptions:

• annual electricity yield from the 0th year of operation of the installation—4102.03 kWh;
• installation efficiency—40%;
• element wear factor—5%;
• total investment cost with energy storage— EUR 9568;
• total co-financing for the installation— EUR 6207;
• wind installation service costs—EUR 230 per year;
• insurance costs—EUR 49 per year;
• planned period of use—25 years;
• electricity purchase price—EUR 0.34/kWh;
• price of energy sales to the grid—EUR 0.18/kWh;
• inflation—5%;
• household energy demand—2500 kWh per year.

Summing up the costs of maintaining solar installation and energy warehouses, it can be stated that annual costs oscillate around EUR 118–236. It is worth noting that these costs may vary depending on the size of the installation, type and capacity of the energy storage and location. The initial years of operation are usually cheaper, thanks to the manufacturer’s guarantee, which covers most components. With time, there may be a need to replace some elements, which may increase the cost of living. Regular reviews and maintenance can, however, significantly extend the life of the installation and energy warehouse, which in the long run reduces the total operating costs.

Investing in a wind installation with energy storage turned out to be a rational step towards improving the energy independence of a household while ensuring the possibility of cost optimization and long-term financial benefits.

Table 6. Summary of costs without taking into account the wind installation.

Year	Energy Consumption	Purchase Price of Electricity	Energy Cost	Discounted Sum
	(kWh)	(EUR)	(EUR/kWh)	(EUR)
0	2500	0.34	−844.83	−844.83
1	2500	0.36	−887.07	−852.95
2	2500	0.37	−931.42	−861.15
3	2500	0.39	−977.99	−869.43
4	2500	0.41	−1026.89	−877.79
5	2500	0.43	−1078.24	−886.23
6	2500	0.46	−1132.15	−894.75
7	2500	0.48	−1188.76	−903.36
8	2500	0.51	−1248.20	−912.04
9	2500	0.53	−1310.60	−920.81
10	2500	0.55	−1376.14	−929.67
11	2500	0.60	−1444.94	−938.61
12	2500	0.62	−1517.19	−947.63
13	2500	0.64	−1593.05	−956.74
14	2500	0.69	−1672.70	−965.94
15	2500	0.71	−1756.34	−975.23
16	2500	0.76	−1844.15	−984.61
17	2500	0.78	−1936.36	−994.08
18	2500	0.83	−2033.18	−1003.63
19	2500	0.87	−2134.84	−1013.29
20	2500	0.92	−2241.58	−1023.03
21	2500	0.94	−2353.66	−1032.86
22	2500	1.01	−2471.34	−1042.80
23	2500	1.06	−2594.91	−1052.82
24	2500	1.10	−2724.65	−1062.94

Source: own study.

shows the projection of electricity consumption costs over 25 years, assuming an annual demand of 2500 kWh. It takes into account rising energy prices, which increase by 5% annually, and a discount rate that decreases over time. Based on these assumptions, the total energy cost in each year and its discounted value were calculated.

The first column of Table 6 is “Year”, which denotes the subsequent years of the analysis, starting from year zero. The second column, “Energy consumption (kWh)”, shows the constant amount of electricity used each year, 2500 kWh by the household. The third column, “Purchase price of electricity (EUR/kWh)”, indicates the expected price of electricity in a given year, which increases at an inflation rate of 5% per year. The fourth column, “Energy cost (EUR)”, shows the total cost of energy consumption in a given year, calculated as the product of consumption and unit price. The last column, “Discounted sum (EUR)”, shows the value of the energy cost after discounting, taking into account the impact of the discount rate on the real value of the amount in a given year. The analysis shows that the total energy cost in the first year is minus EUR 845. In the following years, the price of increased energy results in increasing costs, which, however, are lower in the discounted perspective due to the changing value of money over time. In the last analyzed year, the energy price increased to the level of 1.1 EUR/kWh, which translates into a cost of minus EUR 2725. Nevertheless, the discounted value of this cost is minus EUR 1023, which results from the low discount rate in the final analysis period. The total sum of final costs, after discounting over the entire analyzed period, is minus EUR 23,748 which represents the total financial burden over 25 years.

Table 7. Summary of costs including wind installation for the Pomeranian Voivodeship.

Year	The Amount of Electricity Generated	Amount of Electricity Needed	The Amount of Electricity Transferred to the Grid	Funding	Installation Cost	Service Costs	Insurance	Putting Electricity into the Grid	Sum	Cumulative Cash Flow
	(kWh)	(kWh)	(kWh)	(EUR)	(EUR)	(EUR)	(EUR)	(EUR)	(EUR)	(EUR)
0	4102.03	2500	1602.03	6207	−9568		−48.8	541.37	−2867.94	−2867.94
1	3896.92	2500	1396.92				−48.8	495.67	429.06	−2421.00
2	3702.0.8	2500	1202.08				−48.8	447.86	367.83	−2021.88
3	3516.97	2500	1016.97				−48.8	397.84	308.86	−1672.78
4	3341.13	2500	841.13				−48.8	345.50	252.06	−1376.02
5	4102.03	2500	1602.03			−230	−48.8	690.95	336.20	−963.69
6	3896.92	2500	1396.92				−48.8	632.61	457.03	−379.82
7	3702.08	2500	1202.08				−48.8	571.59	392.90	143.04
8	3516.97	2500	1016.97				−48.8	507.75	331.13	602.06
9	3341.13	2500	841.13				−48.8	440.95	271.63	994.28
10	4102.03	2500	1602.03			−230	−48.8	881.84	401.04	1597.50
11	3896.92	2500	1396.92				−48.8	807.39	484.20	2356.15
12	3702.08	2500	1202.08				−48.8	729.51	417.12	3036.93
13	3516.97	2500	1016.97				−48.8	648.04	352.51	3636.23
14	3341.13	2500	841.13				−48.8	562.78	290.27	4150.27
15	4102.03	2500	1602.03			−230	−48.8	1125.48	459.07	4997.13
16	3896.92	2500	1396.92				−48.8	1030.46	510.89	5978.85
17	3702.08	2500	1202.08				−48.8	931.06	440.80	6861.18
18	3516.97	2500	1016.97				−48.8	827.08	373.29	7639.52
19	3341.13	2500	841.13				−48.8	718.27	308.26	8309.05
20	4102.03	2500	1602.03			−230	−48.8	1436.43	511.75	9466.86
21	3896.92	2500	1396.92				−48.8	1315.15	537.37	10,733.28
22	3702.08	2500	1202.08				−48.8	1188.30	464.20	11,872.84
23	3516.97	2500	1016.97				−48.8	1055.58	393.73	12,879.69
24	3341.13	2500	841.13				−48.8	916.71	325.85	13,747.66

Source: own study.

presents a summary of the analysis of costs related to a wind installation and its energy efficiency over 25 years. It took into account key parameters such as the amount of electricity generated, servicing costs, insurance, subsidies and accumulated cash flows.

In the first year, 4102.03 kWh of electricity was generated, of which 2500 kWh covered its own energy needs, and the surplus of 1602.03 kWh was transferred to the grid. The initial installation cost was minus EUR 9568 and thanks to the funding of EUR 6207 the initial contribution was reduced. The first discounted cash flow was minus EUR 2869 reflecting the initial deficit resulting from the investment. In the following years, we observe stabilization of operating costs, such as annual expenses for servicing (49 EUR) and insurance, as well as a systematic increase in discounted cash flows. For example, in year 10, the energy surplus amounted to 1602.03 kWh, and feeding electricity into the grid generated an additional EUR 402 which resulted in an increase in the discounted sum to EUR 680. In year 20, the installation generated 4102.03 kWh of energy, and the revenues from its feeding into the grid amounted to EUR 512. By this time the total sum of discounted cash flows had reached EUR 4828. At the end of the analyzed period, in year 25, the sum of discounted flows amounted to EUR 6550 which proves the long-term profitability of the installation.

4.3. Comparison of Investment Costs for the Analyzed Investments

When conducting a comparative analysis of the energy efficiency of wind installations in the Pomeranian Voivodeship and the Kraków-Balice region (Lesser Poland Voivodeship), identical assumptions were made regarding the technical parameters of the installations and the assessment methodology. The variables are only differences in location, which allows for a precise assessment of the impact of geographical and climatic conditions on the results of electricity production. Based on meteorological data obtained from the Institute of Meteorology and Water Management (IMGW), significant differences in the energy potential of both regions were noted. There are relatively low and average wind speeds in Poland, in addition, they are varied spatially and temporarily, which affects the overall assessment of wind resources. However, in some regions of the country, especially in the north and on the coast, the wind speeds are high enough, and their daily and annual course can be stable. Such conditions give the possibility of effective use of small wind turbines. Using the digital AMEW-PL atlas, a data package was downloaded in the form of a medium (annual, monthly, daily, hour) report and selected time ranks, taking into account both meteorological and technical characteristics (WPD-theoretical wind energy potential, WEP-generated turbine power), in daily, monthly, season and annual terms. These data allow you to manage the work of an existing installation, e.g., to increase your consumption. The work uses data from the analysis of time ranks of 10 min with a wind speed at an altitude of 10 m above the ground level from the Inca-PL2 model from the period 1/12/2023–30.11.2024. The InCA-PL2 model is a system of ultra-short (newcasting) forecasts based on the modified version of the Inca model (Integrated Nowcasting Through Comprehensive Analysis) of the Austrian meteorological service. The model adapts the Mesoscal forecasts of individual meteorological parameters from the AROME 2.0KM model, with telemetry data from the IMGW-PIB telemetry system. Forecasts and analyses are developed for several fields: temperature at the ground level and 2 m, dew point temperature, relative humidity, snow line, freezing levels, icing, speed and direction of wind at 10 m above sea level. The model in operational mode works with a 10-min time step, while the forecasts are developed and updated with an hour time, and their overtaking time is up to 8 h. The spatial resolution of all Inca-PL2 products is 1 km. For comparative purposes, data from the ERA5-LAND ECMWF Reanalysis V5 model was also used from the same period in 2022. The Pomeranian Voivodeship, characterized by higher average wind speeds and greater stability of atmospheric conditions, shows much higher efficiency of electricity production compared to the Kraków-Balice region, where wind resources are limited. IMWM data indicate that the annual electricity production in the Pomeranian Voivodeship may be even higher 30–50% compared to the Lesser Poland Voivodeship. These differences result from more favorable wind conditions in coastal areas, where wind speeds are higher and more evenly distributed throughout the year. However, in the Kraków-Balice region, frequent changes in wind speed and its lower average values significantly limit the production potential of the installation. The results of the analysis emphasize the key importance of location when designing wind energy investments. Higher production potential in the Pomeranian Voivodeship translates into a faster return on investment costs and higher profitability of the installation compared to the Lesser Poland region. Therefore, the location of the wind installation should be one of the priority factors taken into account when planning the development of renewable energy sources in Poland. Figure 3 shows detailed maps of investment locations, illustrating differences in geographic location and availability of wind resources. Data analysis from wind installation indicates significant differences in energy efficiency between these regions.

The wind installation was connected to the power grid on 1 December 2023, similar to the one in Łeba in the Pomeranian Voivodeship. The analysis covered the full calendar year, covering the period from December 2023 to November 2024. Figure 4 shows the average wind speed for the Kraków-Balice location, based on data obtained from IMWM.

Figure 4 shows the average wind speed for the Kraków-Balice location in the period from December 2023 to November 2024. The data indicate high variability of wind speed over time, with a clear decrease in values in the summer months and moderate wind activity in the remaining months. The highest wind speeds, reaching approximately 30–40 km/h, occur sporadically in the winter months, while in other periods the average wind speed oscillates around lower values, in the range of 5–15 km/h. Compared to Łeba in the Pomeranian Voivodeship, where wind conditions are much more favorable (with higher average wind speed and greater stability throughout the year), the efficiency of the installation in Kraków-Balice will be noticeably lower. Stronger and more regular winds in Łeba will translate into higher electricity production and better profitability indicators of investments in wind installations. Therefore, the choice of location Łeba offers much greater benefits in terms of energy and economic efficiency. Based on Formula (1), the generated electricity was calculated similarly. The calculation results are presented in

Table 8. Electricity was calculated based on data in Małopolska.

Year	Average Wind Speed (km/h)	Average Wind Speed (m/s)	P-Electricity Produced (W)	Electricity Produced (kWh)
01.12.2023	8.5	2.4	51.2	0.7
02.12.2023	14.8	4.2	136.9	3.3
…	…	…	…	…
27.11.2024	4.1	1.2	23.4	0.4
28.11.2024	13.7	3.9	108.6	2.7
29.11.2024	11.5	3.2	64.3	1.6
30.11.2024	10.9	3.1	54.7	1.4

Source: own study.

.

Table 8 presents data on the operation of the wind turbine, taking into account its operating range at wind speeds of 2.5–40 m/s (similarly for the case considered in Łeba) and the efficiency of 40%. At speeds below 2.5 m/s, the turbine remains inactive, which translates into days with zero energy production. As wind speed increases, electricity production increases systematically, reaching maximum values when the wind speed is close to the upper operating limit of the turbine.

Table 9. Summary of costs including wind installation for the Lesser Poland Voivodeship.

Year	The Amount of Electricity Generated	Amount of Electricity Needed	Amount of Electricity Purchased	Funding	Installation Cost	Service Costs	Insurance	Buying Electricity from the Grid	Sum	Cash Flow
	(kWh)	(kWh)	(kWh)	(EUR)	(EUR)	(EUR)	(EUR)	(EUR)	(EUR)	(EUR)
0	1059.72	2500	−1440.28	6207	−9568		−49	−486.71	−3896.03	−3896.03
1	1006.73	2500	−1493.27				−49	−529.85	−555.44	−4302.51
2	956.40	2500	−1543.60				−49	−575.10	−574.93	−4713.80
3	908.58	2500	−1591.42				−49	−622.56	−593.92	−5129.28
4	863.15	2500	−1636.85				−49	−672.35	−612.45	−5548.39
5	10,590.72	2500	−1440.28			−230	−49	−621.19	−733.68	−6074.56
6	1006.73	2500	−1493.27				−49	−676.24	−567.48	−6413.88
7	956.40	2500	−1543.60				−49	−733.99	−588.17	−6762.00
8	908.58	2500	−1591.42				−49	−794.56	−608.35	−7118.11
9	863.15	2500	−1636.85				−49	−858.11	−628.02	−7481.47
10	1059.72	2500	−1440.28			−230	−49	−792.81	−712.32	−7917.54
11	1006.73	2500	−1493.27				−49	−863.07	−581.95	−8205.32
12	956.40	2500	−1543.60				−49	−936.77	−603.83	−8505.27
13	908.58	2500	−1591.42				−49	−1014.09	−625.15	−8816.45
14	863.15	2500	−1636.85				−49	−1095.18	−645.94	−9137.94
15	1059.72	2500	−1440.28			−230	−49	−101185	−699.54	−9503.03
16	1006.73	2500	−1493.27				−49	−1101.52	−598.60	−9751.66
17	956.40	2500	−1543.60				−49	−1195.59	−621.65	−10,015.40
18	908.58	2500	−1591.42				−49	−1294.26	−644.10	−10,293.13
19	863.15	2500	−1636.85				−49	−1397.76	−666.00	−10,583.81
20	1059.72	2500	−1440.28			−230	−49	−1291.40	−693.95	−10,893.28
21	1006.73	2500	−1493.27				−49	−1405.86	−617.22	−11,112.63
22	956.40	2500	−1543.60				−49	−1525.91	−641.43	−11,349.65
23	908.58	2500	−1591.42				−49	−1651.84	−665.02	−11,603.09
24	863.15	2500	−1636.85				−49	−1783.94	−688.01	−11,871.79

Source: own study.

contains a summary presenting the analysis of costs related to the operation of a wind installation and its energy efficiency over 25 years. The summary includes key indicators such as the amount of electricity produced, service costs, insurance expenses, the amount of subsidy and discounted cash flows.

Table 9 presents an analysis of the operating costs and energy efficiency of a wind installation over 25 years. The results indicate that the amount of electricity generated ranges between 863.15 kWh and 1059.72 kWh per year, which is significantly lower than the annual energy demand of 2500 kWh. The energy deficit forces the purchase of energy from the grid in amounts ranging from 1440.28 kWh to 1636.85 kWh per year, which significantly increases operating costs. Despite an initial subsidy of EUR 6207 in the first year, installation costs and related expenses, such as servicing (fixed fee 49 EUR per year) and purchase of energy from the grid, resulted in a systematic increase in the financial deficit. Energy purchase costs increase over time, from an initial 487 EUR to EUR 1785 in the 24th year. Cash flows remain negative throughout the analyzed period, indicating the lack of profitability of investments in this configuration. The discounted sum increases negatively from EUR −3897 in the first year to EUR −19,064 in the 25th year, reflecting the long-term financial burden resulting from insufficient electricity production compared to needs. The analysis indicates the need to improve the efficiency of energy production or reduce operating costs to increase the profitability of the project.

4.4. Analysis of the Profitability of Investing in a Wind Turbine Using the NPV and IRR Method for the Studied Locations

The profitability of the investment was calculated according to the accumulated cash flows (Table 4). Figure 5 shows the cumulative cash flows.

Figure 5 shows the change in the profitability of investing in a wind installation over time. As shown by the data presented, the investment has been profitable for the 9th year. In the following years, wind installation begins to generate increasing profits, which means no additional costs for electricity needed to power home appliances, such as an induction cooker or charging electronic devices (e.g., laptops, mobile phones). For the ninth year, the installation not only covers its costs but also generates income, which increases significantly in subsequent years. Still using the IRR Formula (5):

$${\sum }_{i=1}^n{\displaystyle \frac{P_i }{{\left(1+IRR\right)}^n}}=0$$

(5)

$\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}:$

• $P_i$—payment for the period i,
• n—number of periods,
• IRR—one-year interest rate.

$$\begin{gathered} {\displaystyle \frac{-2867.94 }{{(1+IRR)}^0}}+{\displaystyle \frac{-2421.00}{{(1+IRR)}^1}}+{\displaystyle \frac{-2021.88}{{(1+IRR)}^2}}+{\displaystyle \frac{-1672.78}{{(1+IRR)}^3}}+{\displaystyle \frac{-1376.02}{{(1+IRR)}^4}}+{\displaystyle \frac{-963.69}{{(1+IRR)}^5}}+{\displaystyle \frac{-379.82}{{(1+IRR)}^6}}+{\displaystyle \frac{143.04}{{(1+IRR)}^7}} \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+{\displaystyle \frac{602.06}{{(1+IRR)}^8}}+{\displaystyle \frac{994.28}{{(1+IRR)}^9}}+{\displaystyle \frac{1597.50}{{(1+IRR)}^{10}}}+{\displaystyle \frac{2356.15}{{(1+IRR)}^{11}}}+{\displaystyle \frac{3036.93}{{(1+IRR)}^{12}}}+{\displaystyle \frac{3636.23}{{(1+IRR)}^{13}}} \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +{\displaystyle \frac{4150.27}{{(1+IRR)}^{14}}}+{\displaystyle \frac{4997.13}{{(1+IRR)}^{15}}}+{\displaystyle \frac{5978.85}{{(1+IRR)}^{16}}}+{\displaystyle \frac{6861.18}{{(1+IRR)}^{17}}}+{\displaystyle \frac{7639.52}{{(1+IRR)}^{18}}}+{\displaystyle \frac{8309.05}{{(1+IRR)}^{19}}} \\ \hspace{1em}\hspace{1em}\hspace{1em}+{\displaystyle \frac{9466.86}{{(1+IRR)}^{20}}}+{\displaystyle \frac{\mathrm{10,733.28}}{{(1+IRR)}^{21}}}+{\displaystyle \frac{\mathrm{11,872.84}}{{(1+IRR)}^{22}}}+{\displaystyle \frac{\mathrm{12,879.69}}{{(1+IRR)}^{23}}}+{\displaystyle \frac{\mathrm{13,747.66}}{{(1+IRR)}^{24}}}=2868.05 \end{gathered}$$

The IRR coefficient was 14.94%, which means that the expected annual rate of return on the investment is at a very favourable level. This result indicates that the project is generating sufficient cash flow to cover financing costs and generate excess profit. This result is much higher than the adopted discount rate of 4%, which confirms the profitability of the investment. The investment not only meets the profitability criteria but also exceeds standard expectations regarding the rate of return, which makes it competitive compared to other forms of capital investment. This result indicates a solid financial outlook for the project, although it is worth ensuring that cash flow assumptions are realistic and take into account potential risks. In the further part of the research, NPV was calculated based on Formula (6):

$${\sum }_{t=0}^n{\displaystyle \frac{C_t }{{\left(1+r\right)}^t}}=NPV$$

(6)

$\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}:$

• $C_t$—cash flows from investment,
• t—number of periods in which the flow occurs,
• r—internal rate of return.

$$\begin{array}{l}\frac{-2867.94}{(1+r{)}^0}+\frac{-2421.00}{(1+r{)}^1}+\frac{-2021.88}{(1+r{)}^2}+\frac{-1672.78}{(1+r{)}^3}+\frac{-1376.02}{(1+r{)}^4}+\frac{-963.69}{(1+r{)}^5}+\frac{-379.82}{(1+r{)}^6}+\frac{143.04}{(1+r{)}^7}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +\frac{602.06}{(1+r{)}^9}+\frac{994.28}{(1+r{)}^{10}}+\frac{1597.50}{(1+r{)}^{11}}+\frac{2356.15}{(1+r{)}^{12}}+\frac{3036.93}{(1+r{)}^{13}}+\frac{3636.23}{(1+r{)}^{14}}+\frac{4150.27}{(1+r{)}^{15}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +\frac{4997.13}{(1+r{)}^{16}}+\frac{5978.85}{(1+r{)}^{17}}+\frac{6861.18}{(1+r{)}^{18}}+\frac{7639.52}{(1+r{)}^{19}}+\frac{8309.05}{(1+r{)}^{20}}+\frac{9466.86}{(1+r{)}^{21}}+\frac{10,733.28}{(1+r{)}^{22}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +\frac{\mathrm{11,872.84}}{(1+r{)}^{23}}+\frac{\mathrm{12,879.69}}{(1+r{)}^{24}}=\mathrm{41,347.03}\end{array}$$

Using Excel, the data was entered into a spreadsheet and discounted annually using a rate of return assumed at 4%. Then the discounted cash flows were added and the NPV was calculated. The results of the analysis of IRR and NPV indicators for a wind installation indicate the profitability of the investment. The IRR value is 14.94%, which exceeds the assumed discount rate of 4%, which means that the project generates a rate of return exceeding the cost of capital. Additionally, the NPV value of EUR 41,347.03 confirms that the investment’s cash flows, after taking into account financing costs, bring a surplus. Both indicators indicate that the project is profitable and the investment ensures both high profit and financial security. Verifying the correctness of the NPV calculations requires replacing the limit rate with the value obtained from the first calculation method, which is 14.94%. At the final stage, the value of discounted cash flows was added up and the value was 0. After applying a rate of return of 14.94%, the NPV indicator reached the value of 0. This means that the investment is financially neutral, generating neither profits nor losses resulting from the allocation of capital. The NPV indicator equal to zero also confirms the correctness of the calculations performed in individual methods. If the IRR is used as the cut-off rate in the NPV calculation, the result should be 0.

4.5. Summary of the Profitability Assessment of the Tested Investment Model

The presented model of a home wind installation with a capacity of 2 kW and the use of energy storage with a capacity of 7.5 kWh allowed for the return of the invested capital. Profitability was estimated over 25 years of operation, which results from the expected life of key components of the installation, such as the wind turbine and energy storage, which are covered by a manufacturer’s warranty for 10 years. The NPV and IRR methods were used to analyze the profitability of the investment. The NPV method showed a positive net present value, confirming that the investment is profitable, taking into account initial costs of EUR 9567.48 and annual operating costs of EUR 279 (including service and insurance). In turn, the calculated internal rate of return IRR exceeded the discount rate assumed at 4%, which indicates the high profitability of the project. Forecasts of electricity production were based on meteorological data from Łeba, where the average wind speed is 4.5 m/s, and the installation achieved an annual efficiency of 4102.03 kWh in the first year of operation. It is worth adding that the energy storage system allowed for the optimization of the consumption of electricity produced by maximizing auto consumption, which amounted to 40% of total production. Variable electricity prices were estimated based on historical price data, with the unit price of electricity from the grid being EUR 0.34/kWh and surplus energy sold to the grid at a rate of EUR 0.18/kWh. To assess the variability of costs, an inflation factor of 5% was adopted, which enabled reliable forecasting of economic results in the long term. The investor decided to implement a micro wind installation supported by the “My Wind Power Plant” program and thermal modernization relief. The funding obtained amounted to a total of EUR 6207, which significantly shortened the investment payback time. As a result, the total payback time was reduced to seven years, assuming stable wind conditions and moderate household energy consumption (2500 kWh per year). Potential decreases in system efficiency resulting from the wear of installation components were also taken into account, at the level of 5% per year. Additionally, the conducted analyses emphasized the importance of the turbine location, taking into account wind conditions and the surroundings, which had a key impact on the energy and economic efficiency of the system.

5. Conclusions

The profitability analysis carried out confirmed the commonly accepted view that investments in renewable energy sources pay off within a few years. The awareness that renewable energy is the future, and the need to protect the natural environment forces both the demand and supply sides to take action to support initiatives related to the integration of energy systems in residential buildings. Based on the literature review and our research, the following conclusions were drawn:

• The analysis of NPV and IRR indicators for investments in home micro wind installations, carried out in the work, confirms the validity of investing capital in this type of project, demonstrating their high profitability and attractive rates of return, which results from the effective use of renewable energy sources;
• The analysis showed that the payback period is 7 years thanks to financial support from the “ My Wind Farm” program and tax reliefs. Without this support, the payback period would be longer, but still profitable. The return period applies only to the Pomeranian location because the second tested location is not profitable;
• The use of energy storage increases the efficiency of the system by optimizing auto consumption. Investing in such a system is particularly beneficial in regions with moderate wind conditions;
• Government support programs such as “Moja Elektrownia Wiatrowa” thermal modernization relief, significantly increase the availability and profitability of investments in renewable energy sources. Continued support of this type is expected to encourage new investment in the future.

At this stage of summarizing it is important to remember that energy obtained from wind is characterized by high variability of output power and low availability, so it is necessary to predict their future energy production for economic purposes. As part of future work, forecasting methods should be developed and investigated to increase the accuracy of wind farm power prediction using artificial intelligence methods. The potential of different Gaussian Process Regression (GPR) models based on kernel functions should be explored. As a result of the research, various structures of forecasting models should also be tested and the most advantageous solution variant should be selected. In a sea of data, machine learning methods can effectively create predictive models without the need for tedious analyst intervention in data preparation and multi-stage analysis. Furthermore, future research should focus on testing and using other algorithms such as XGBoost, evolutionary polynomial regression and gene expression programming, for predicting wind farm energy production. Certainly, such research will be the subject of the author’s future work.

In summary, the considerations presented do not exhaust the entire topic concerning the evaluation of the energy potential and economic efficiency of a home wind installation: an economic perspective on purchasing a wind turbine. According to the authors, further broader study in this research area may determine the future development of this form of energy acquisition. Pointing out not only the economic benefits but also the energy, environmental and social benefits arising from the use of integrated renewable energy systems in currently used residential buildings.